{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<small>\n",
    "Copyright (c) 2017 Andrew Glassner\n",
    "\n",
    "Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the \"Software\"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:\n",
    "\n",
    "The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.\n",
    "\n",
    "THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.\n",
    "</small>\n",
    "\n",
    "\n",
    "\n",
    "# Deep Learning From Basics to Practice\n",
    "## by Andrew Glassner, https://dlbasics.com, http://glassner.com\n",
    "------\n",
    "## Chapter 17: Activation Functions\n",
    "### Plots of Activation Functions\n",
    "\n",
    "This notebook is provided as a “behind-the-scenes” look at code used to make some of the figures in this chapter. It is still in the hacked-together form used to develop the figures, and is only lightly commented."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "import seaborn as sns ; sns.set()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Library/Frameworks/Python.framework/Versions/3.5/lib/python3.5/site-packages/h5py/__init__.py:34: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n",
      "  from ._conv import register_converters as _register_converters\n",
      "Using TensorFlow backend.\n"
     ]
    }
   ],
   "source": [
    "# Make a File_Helper for saving and loading files.\n",
    "\n",
    "save_files = True\n",
    "\n",
    "import os, sys, inspect\n",
    "current_dir = os.path.dirname(os.path.abspath(inspect.getfile(inspect.currentframe())))\n",
    "sys.path.insert(0, os.path.dirname(current_dir)) # path to parent dir\n",
    "from DLBasics_Utilities import File_Helper\n",
    "file_helper = File_Helper(save_files)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "matplotlib.rcParams['axes.titlesize'] = 14\n",
    "matplotlib.rcParams['axes.labelsize'] = 14\n",
    "matplotlib.rcParams['axes.labelpad'] = 8\n",
    "matplotlib.rcParams['xtick.labelsize'] = 14\n",
    "matplotlib.rcParams['ytick.labelsize'] = 14\n",
    "\n",
    "af_clr = '#D12927'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def make_linear_trio():\n",
    "    plt.figure(figsize=(10,3))\n",
    "    plt.subplot(1, 3, 1)\n",
    "    plt.plot([0,1],[0,1], lw=3, color=af_clr)\n",
    "    plt.xticks([0,.5,1],[0,.5,1])\n",
    "    plt.yticks([0,.5,1],[0,.5,1])\n",
    "    plt.title('(a)')\n",
    "\n",
    "    plt.subplot(1, 3, 2)\n",
    "    plt.plot([0,1],[.7, .4], lw=3, color=af_clr)\n",
    "    plt.xticks([0,.5,1],[0,.5,1])\n",
    "    plt.yticks([0,.5,1],[0,.5,1])\n",
    "    plt.title('(b)')\n",
    "\n",
    "    plt.subplot(1, 3, 3)\n",
    "    plt.plot([0,1],[.1, .3], lw=3, color=af_clr)\n",
    "    plt.xticks([0,.5,1],[0,.5,1])\n",
    "    plt.yticks([0,.5,1],[0,.5,1])\n",
    "    plt.title('(c)')\n",
    "    file_helper.save_figure('linear-trio')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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lxhxIOv4RJiIiIgoWV1REUcr17T6UPjcVcMoHIsudI5Eyax4HIiIiIqIQ4aqKKAq5vj8A\n28xnIOx2Wd3y4zuROns+JL1eoc6IiIiItIdDEVGUcR36HrZnJ0PYa2R1S86Pkfr8QkgGg0KdERER\nEWkThyKiKOL+IR+2GZMhqqtldfPgoUh94RUORERERERhwKGIKEq4D/+AkulPQ1RVyurmgdlIe2kx\nJKNRoc6IiIiItI1DEVEUcB89DNu0SRAV5bK6qf9ApC14DZLJpFBnRERERNrHoYhIYZ4Tx2GbNgm+\n8jJZ3dTvNlhfWQrJbFaoMyIiIqLYwKGISEGe4iKUTJ0IX6lNVjf1vQVpi16HZLYo1BkRERFR7OBQ\nRKQQz6lilEyZCF/JRVnd2Lsv0havhC4uTqHOiIiIiGILhyIiBXjOnIZt6kT4LpyX1Y29esP62kro\n4uMV6oyIiIgo9nAoIoow77mzsE2ZCO+5s7K6MbMnrEtXQZeQqFBnRERERLGJQxFRBHkvnEfJ1Inw\nnj0tqxu6Z8K6/C3oEjkQEREREUUahyKiCPGWXETJlInwniqW1Q1duyN9+VvQJSUr1BkRERFRbONQ\nRBQBXluJfyAqLpLVDZ27wPr6auhSUhXqjIiIiIg4FBGFmbesFLZpT8FbdFxW13foBOvrb0OfmqZM\nY0REREQEgEMRUVj5ystgmzYJnmNHZXV9uw5IX/kO9NZ0hTojIiIioks4FBGFia+yAiXTn4bnSKGs\nrm/TFukr3oY+vYVCnRERERHRlTgUEYWBr6oKthmT4SkskNX1rdsgfeUa6DNaKdQZEREREV2NQxFR\niPmqq2B79tdw5x+U1XUZrWBd+Q70rVor1BkRERER1YdDEVEI+WpqYJs1Be6DB2R1XcsMpK9cA8MN\nbRTqjIiIiIgawqGIKER8djtKZ0+F+8B+WV2X3gLpK96GoW07hTojIiIiomvhUEQUAsLpQOmcaXDt\n2yur69KssL7+NgztOyrUGRERERFdD4cioiAJpxO2uc/CtXePrK5LSYX19dUwduqsUGdERERE1Bgc\nioiCIFwulL4wC67dO2V1KTnFPxB16aZQZ0RERETUWByKiJpJuN0onT8bzp15srqUmIT05W/B2K2H\nQp0RERERUVNwKCJqBuHxoGzBXDjzcmV1KSEB1mVvwtgjS6HOiIiIiKipOBQRNZHweFD28jw4cr+U\n1aW4eFiXrIKp540KdUZEREREzcGhiKgJhNeLslfnw/HlZlldiouDdckbMN3UR6HOqDnO/+53cHy1\nE8LtVroVIiIiUpBB6QaI1EL4fChfshCOzf+WbzCbkbZ4BUx9blamMWq2s8uXAvB/7NE8YBAs2cNg\nHjgYuqRkhTsjIiKiSOJQRNQIwudD+bJFsG/aKN9gMsP66usw33yrMo1RSIjqaji+3Oy/AqjXw9Tn\nFliG5MCcnQPDDW2Vbo+IiIjCjEMR0XUIIVCxYgnsGz+WbzAaYX1lKcy3DlCmMQoPrxeub/bA9c0e\n4M3XYejcFZYhw2DOzoExsyckHT91TEREpDUcioiuQQiBijeWoeaTD+UbDAakvbwU5gGDlGmMQiK+\nT1/UfLv/mj/jOXYEVceOoGr9OujSW8AyeCjM2Tkw97sNktkSoU6JiIgonDgUETVACIHK1StRs+ED\n+Qa9HmkLFsMyMFuZxihkuv3lr7hYeBzVW3PhyMuF8+vdgMvZ4M/7Si6i5tMNqPl0AySLBab+A2HJ\nzoF50BDoU9Mi2DkRERGFEocionoIIVD57luo/tuf5Bv0eqS+uAiW7GHKNEYhp2/REvH33If4e+6D\nz26Ha88u/4C0Yxt8ZaUN7iccDji3/gfOrf8BdDoYb+wDS3YOLNlDYejQKWL9ExERUfAkIYRQuolg\nlJZWw+PxKd0GNZPBoENaWkJUvY5CCFT9bg2q1q+Tb9DpkDpvIeKG/0SZxqLYpddRjRo694TXC/fB\n7+DI819F8hYdb/Qx9R06wjI4B5bsHBhv7A1Jrw9hx3SlaMwQajo1ZwjAtYjaMUe0Idgc4VBEiorG\nIKr8/W9Q9d5aeVGSkDr3JcSNuEuZpqKcmhc0jT33PCdP+K8g5W2F67v9gK9x56suJRXmQUNgyc6B\nqf9A6OLigm2ZrhCNGUJNp+YMAbgWUTvmiDZwKOIJrGrRFkRV699D5W/flhclCSnPvYD4n45WpikV\nUPOCpjnnnresFM6deXDm5cK5eyeE3d64HU0mmG8dUHezBn16i2Z0TFeKtgyh5lFzhgBci6gdc0Qb\nOBTxBFa1aAqiqj+vR+WaVQH1lJnPI37UGAU6Ug81L2iCPfeE0wnnN3vgrP2Yna/kYqP3Nfa8EeZs\n/8fsDJ27QpKkZvcRq6IpQ6j51JwhANciascc0QYORTyBVS1agqjqgz+hcvWKgHrytOeQMGasAh2p\ni5oXNKE894TPB3fBITi358KxLReeo4cbva/+hja1A9IwmPrcDMnA++A0RrRkCAVHzRkCcC2idswR\nbeBQxBNY1aIhiKo/+gAVbywNqCc/8ywS7h+nQEfqo+YFTTjPPc+ZU3DmbYUjbwtc+78BvN5G7Scl\nJsE8cDAs2cNgvn0QdAmJYelPC6IhQyh4as4QgGsRtWOOaAOHIp7AqqZ0EFV/8hEqlr8aUE+aNBWJ\n4x6IeD9qpeYFTaTOPV9lBZy7dsCRtwXOXdshqqsbt6PBANPNt8IyJAeWwTnQt2od3kZVRukModBQ\nc4YAXIuoHXNEGzgU8QRWNSWDqGbjxyhf8nJAPemJyUh84KGI9qJ2al7QKHHuCbcbrv174diWC+f2\nXHjPnW30vobumbXPQ8qBoXtmzH8PiYsZbVBzhgBci6gdc0QbOBTxBFY1pYKoZtNnKF+8ALjq9E/8\n1UQkPfhIxPrQCjUvaJTOECEEPEcK4di2Bc7tW+EuONTofXUtM+oGJNPNt0IymcLYaXTiYkYb1Jwh\ngPI5QsFhjmgDhyKewKqmRBDZP9+EsldeCByIJjyGpIcfj0gPWqPmBU20ZYj3/Dk4tm/13+77mz2A\n292o/aT4BJgHDII5eygsA7OhS04Jc6fRgYsZbVBzhgDRlyPUNMwRbeBQxBNY1SIdRPYvPkfZwucD\nHryZMP5hJP1qYsx/FKm51LygieYM8dVUw/nVTv/tvnfmQVSUN25HvR6m3jdfvt1323bhbVRBXMxo\ng5ozBIjuHKHrY45oA4cinsCqFskgsud+gbL5cwLuAJbw8weR9ORkDkRBUPOCRi0ZIjweuL7bX/c8\nJO+p4kbva+jcBebB/gHJ2PNGSDpdGDuNLC5mtEHNGQKoJ0eofswRbeBQxBNY1SIVRI68LSidNytw\nIPqfXyBp0lQOREFS84JGjRkihIDnxLG6Acl98LuAj4M2RGe1wjxoKCzZOTDfNgCS2RLmbsOLixlt\nUHOGAOrMEbqMOaINHIp4AqtaJILIsTMPpXNnAB6PrB5/3zgkPzODA1EIqHlBo4UM8ZZchHNnnv9m\nDXu+AlzOxu1oNsPcfyAsg3NgHjwE+jRreBsNAy5mtEHNGQJoI0diGXNEG4LNET4ynTTNuXsnSufN\nDByI7r2fAxFphj69BeJHjUH8qDEQDgecX++qvd33VvjKShve0emEc9sWOLdtASQJxht7197Nbhj0\nHTryzwcREcUMXikiRYXz3Rnn11/B9ty0gHfN40aNQcqMOZr6XoXS1Pwur5YzRHi9cB/6Ho7tuXBu\ny4XnxLFG76tv1wGW7KGwZA+D8cbekAzR+R4a3+HVBjVnCKDtHIkFzBFt4MfneAKrWriCyLnva9hm\nPgM4rxqIRo5CynMvcCAKMTUvaGIpQzzFRXDk5cKZlwvXgf0Bd2FsiJSSAsvAITAPyYH5toHQxceH\nudPG42JGG9ScIUBs5YgWMUe0gUMRT2BVC0cQub7dB9vMX0PY7bK65c6RSJ3zEiS9PiS/hy5T84Im\nVjPEV14Gx448OLfnwvnVjoA/Lw0yGmHu1x/mIcNgGTwU+hYtw9vodXAxow1qzhAgdnNEK5gj2sCh\niCewqoU6iFzfH4Bt+tMQ9hpZ3fLjO5H6/MKo/QiQ2ql5QcMMAYTTCec3e+DM2wrH9lz4Ll5o9L7G\nzJ7+ASk7B4Yu3SL+PSQuZrRBzRkCMEfUjjmiDRyKeAKrWiiDyJV/ELZpT0FUV8vqlpwfI/XFRRyI\nwkjNCxpmiJwQAu6CQ/7bfW/PhedwYaP31bduA3O2/3bfpr79IvJnjosZbVBzhgDMEbVjjmgDhyKe\nwKoWqiBy/1CAkqkTIaoqZXXz4KFIW/AaJKMx2FbpGtS8oGGGXJvnzGk4t2+FIy8Xrn1fBzzrqyFS\nYiLMt2f7n4c0YBB0SUlh6Y+LGW1Qc4YAzBG1Y45oA4cinsCqFoogch8pRMmUiRAV5bK6eWA20hYu\ngWQyhaJVugY1L2iYIY3nq6qCc9d2/80aduVBVFU1bke9Hqabb/UPSNk5MLS+IWQ9cTGjDWrOEIA5\nonbMEW3gUMQTWNWCDSL3sSOwPfMkfOVlsrqp/0BYX1kGyWwOVat0DWpe0DBDmke43XB9+03d3ey8\nZ880el9Dt+7+B8Zm58CY2TOo7yFxMaMNas4QgDmidswRbeBQxBNY1YIJIs+J4yiZ8gR8Npusbup3\nG6yLV0AyW0LZKl2Dmhc0zJDgCSHgOXrYPyBt2wJ3waFG76trmQHLoKEwZw+FuV//Jl/Z5WJGG9Sc\nIQBzRO2YI9rAoYgnsKo1N4g8xUUo+fUT8JVclNVNfW9B2mtvQBcXF+pW6RrUvKBhhoSe98J5OHZs\ng3PbFjj37gbc7kbtJ8XFwzxgIMzZw2AZOBi6lNTr7sPFjDaoOUMA5ojaMUe0gUMRT2BVa04QeU4V\no+SZJ+C7cF5WN/buC+uSVVH1YMlYoeYFDTMkvHw1NXDu2Qnntlw4dm6DKC+//k4AoNPB1Luvf0DK\nzoGhXft6f4yLGW1Qc4YAzBG1Y45oA4cinsCq1tQg8pw5DdszT8B77qysbuzVG9Zlq6BLSAxXq3QN\nal7QMEMiR3g8cH9/AI68LXBsy4X31MlG72vo2Ln2dt/DYOx5Y91DmLmY0QY1ZwjAHFE75og2cCji\nCaxqTQki77mzKPn1E/CePS2rGzN7wvr629AlciBSipoXNMwQZQgh4C064R+Q8nLh/v4A0Mi/jnRp\nVpgHDYFlSA7ibx+I9Bta8HVUOTVnCMAcUTsORdrAoYgnsKo1Noi8F86j5Jkn4D1VLN+/eybSV7wN\nXVJyuFula1DzgoYZEh28pTY4t2+DY3sunLt3Ak5no/aTzGYkDc6G/vZsGG/Pht6aHuZOKRzUnCEA\nc0TtOBRpA4cinsCq1pgg8pZc9F8hKi6S79u1u38gasSXsSm81LygYYZEH+F0wLnnK//d7HZsDbjD\nZIMkCcaeN8EypPZ5SB07B3W7b4ocNWcIwBxROw5F2sChiCewql0viLy2EpQ88yS8Rcfl+3XuAuvK\nNdCnpkWoU7oWNS9omCHRTfh8cB/63j8gbc+F59jRRu+rb9uu7oGxppv6QjIYwtgpBUPNGQIwR9SO\nQ5E2cCjiCaxq1woib1kpbFOeDFgE6Tt0Qvoba/gxmSii5gUNM0RdPKeK6x4Y6zqwD/B6G7WflJwC\ny8BsmLNzYB4wELp4dZ6vWqXmDAGYI2rHoUgbOBTxBFa1hoLIV16GkqlPwXOkUPbz+nYdkL7qXejT\nW0S6VboGNS9omCHq5Ssvg3vPTnh35aEiNxfCXtO4HY1GmG+5DebsHFiyc6BvmRHeRum61JwhAHNE\n7TgUaYMiQ1FZWRnefPNNfPnllygpKUGnTp3w0EMPYezYsdfdd8OGDZg9e3a92+677z68+uqrTeqF\nJ7C61RdEvsoK/0BUWCD7WX2btkh/413oM1op0SpdQ1ODiBlCoXLp3LOdK0XNnt1w5OXCkZcb8Byz\nazFm9oR58FBYhgyDoWt3fg9JAc1ZzDBHKFQ4FGlDsENRkz9gbbfb8cgjj6CwsBDjx49H586d8a9/\n/Qtz585FSUkJHn/88WvuX1BQAEmSsGjRIhiu+nx3hw4dmtoOaYyvqgq2GZMDB6LWbZC+cg0HIg1g\nhlA4SCYTzAMGwTxgEJKnzISnsMA/IG3bAs/hH665r7vgENwFh1D13lroW7WGebD/CpLp5n6QjMYI\n/RdQUzCljOBJAAAgAElEQVRHiCjUmnylaO3atVixYgWWL1+Ou+++u67+6KOPYvfu3fj888/RqlXD\nC9cJEybg2LFj2LJlS/O7vgKnenW78t0ZV3kFbDN+DffBA7Kf0WW0QvqqtTDc0EahLul6mvLuDDOE\nQqlRd7A8dxaO7blwbMuFa9/XgMfTqGNLCQkw3z4YluxhMN8+GLqkpFC2Tldo6ju8zBEKJV4p0oZg\nrxTpmrrDxx9/jJYtW8pCCPAHkcvlwqeffnrN/QsKCtC9e/em/lrSOF9NDWyzpgQORC0zkL5yDQci\nDWGGUKTpW7VGwn3jkL78LbT6+HOkvrgIljtHQkq89pAjqqvh+OJzlC18HufGjEDJ1Imo/vtf4Dlz\nKkKdU0OYI0QUak36+FxVVRWOHj2KO+64I2Bbnz59AADffvttg/ufP38epaWldUHkdrshhIDJZGpK\nG6QxvpoaXJw5Be4D+2V1XXoLpK94G4a27RTqjEKNGUJK0yUmIm74CMQNHwHh8cD17T448rbAuS0X\n3rOnG97R64Vr7x649u4B3lwOQ5du/uchDc6BMbMnJF2T32OkZmKOEFE4NGkoOnfuHIQQaN26dcC2\nxMREJCQkoLi4uMH98/PzAQDFxcW4//77UVBQAJ/Ph5tuugnTpk3DoEGDmtg+qZ3P6cDxadPh/OZr\nWV2XZkX6indgaN9Roc4oHJghFE0kgwHmfrfB3O82iKenwXPsSN3tvt2Hvr/mvp6jh1F19DCq/rAO\nuhYtYRk81H+771tug2Q2R+i/IDYxR4goHJr01lZlZSUAICGh/s/rxcXFoaam4VuiFhT4vzz/zTff\nYPTo0Vi9ejVmzpyJM2fO4NFHH8XmzZub0g6pnHA6UfLcdFTt2imr61JSYV3xNgwdOynTGIUNM4Si\nlSRJMHbphqQHH0GLNb9Hxof/RMr02TAPGgJc5wqC7+IF1HzyEUpnTcG5MSNQOm8majZ9Bl9ZWYS6\njy3MESIKhyZdKbrePRmEENDr9Q1uv/nmmzFx4kSMHTsW7dr5PxL1ox/9CCNHjsTo0aOxYMEC3HHH\nHbwdagwQLhdKX5gF51fygUhKToH19dUwdu6qUGcUTswQUgt9i5aIv/d+xN97P3x2O1y7d/qvIu3Y\nBl95w8OOsNvhyP0SjtwvUa7TwXhjH1iG+O9mxyvfocEcIaJwaNJQdOldGbvdXu92u92O9u3bN7h/\n//790b9//4B6mzZtMGLECHzyyScoKChAVlZWo3vS6/k5brURbjcuvjQHzp15srqUlISMlathymz8\n60/RobF/DpkhFGqXXr+wvo5JCTANvwOJw++A8Hrh+u5b2Lflwr51CzwnTzS8n88H94F9cB/Yh8p3\nVsHQsRPihgxD3JAcmG7sDekaC/dY05TXjzlCoRaRHKGwC/b1a9JQ1K5dO0iShLNnzwZsq6qqQk1N\nTb2f8W2M9PR0AEB1dXWT9ktOjmvW7yNlCLcbJ2Y8B8c2+W1QdYmJ6PLbdYjv3VuhzigSmCEULhF9\nHX80xP8P5sBx7CgqvvgSFV9+gZpv9gLXuIrhOXEclSeOo/KP70NvtSJ52I+Q/OPhSBo8GLr4+Mj1\nr3LMEQoXvo6xrUlDUXx8PLp27YrvvvsuYNu+ffsAAP369Wtw/yeffBLHjh3DZ599BuNVD8Q7fPgw\nAKBjx6Z9vKCiwg6vl/eUVwPh8aDkpedh/+JzWV2XkICMlavhbNcFztKm/UVE0UGv1zXqLxNmCIXa\npXNPsdcxtRWM9/8c6ff/HKmlpXBs3wr7ti1wfLUTwuFocDevzYbSDR+hdMNHkExmmPsPQNyQHMRl\n50Cf3iKC/wHRobEZAjBHKPQUzxEKiabkSH2aNBQBwL333osVK1bgn//8Z93zAYQQWLduHcxmc8Az\nA67UsmVLbNmyBX/729/wwAMP1NV37dqFrVu3YujQoWjRoml/GXi9Pj5oSwWE14uyRS/CcdVAJMXF\nofOatXB1yeLrGCOYIRQOUfE6JqXAPHI0zCNHQzgdcO7dA2deLhx5ufDZShrcTbiccORthSNvK0rx\nCoy9boJlcA7MQ3Jg6NSF322pB3OEwoGvY2yTxPW+sXgVp9OJsWPHoqioCOPHj0fnzp2xceNG7Nq1\nC7NmzcKECRMA+O/uUlBQgMzMTGRmZgLwPxtg3LhxuHjxIu677z7cdNNNKCwsxF//+le0aNECf/zj\nH9GmTdMe0smnD0c/4fOh/LUFsG/aKN9gNqPl8jdxw/Acvo4q15SnSDNDKJTU8CR64fPBXXDIPyBt\n2wLPsSON3lffpi0s2TkwZw+DqXdfSIYmv5epCk19Ej1zhEJJDTlC19fUHLmafv78+fOb9gsNuOuu\nu1BWVoZNmzbhiy++QHx8PGbOnImf/exndT/3l7/8BYsWLUJ6ejoGDBgAwP/lyHvuuQeVlZXYsmUL\nNm3ahLNnz+Luu+/GsmXL0KpVqyb/Bzgcbvh8TZrrKIKEz4fyZYtg/9dVTxc3mWFd/DribxuAuDgT\nX0eV0+kkxMU17sGHzBAKpUvnXjS/jpIkQd8yA+Z+/ZHwX/+NuJF3w9CmLYTbDe+Fc9f8HpKorIT7\n4Hewb/oM1Rv+BvfRw4DXB31GBiQNPWy0KRkCMEcotNSQI3R9Tc2RqzX5SlG04VQfvYQQqHj9NdR8\n8qF8g9EI66LlMA8YxHdnNCLYd2eUxHNP3dSeIb7KCjh3bocjbwucu3ZA1DTye5UGA0y33AZLdg4s\n2UOhz2jejQWihZozBGCOqJ3ac4T8gs0RDkUUFkIIVLyxDDUbPpBvMBiQ9soyWAZm1/5PBpEWqHlB\nw3NP3bSUIcLthmvf13Bc+h7S+XON3tfQPROWIcNgGZwDQ/ceqvsekpozBGCOqJ2WciSWcSjiCRx1\nhBCoXL0S1X/7k3yDXo+0ha/Bkj2srsQg0gY1L2h47qmbVjNECAFP4Q9wbPcPSJ4f8hu9ry6jVe0V\npByYbr4V0lV3WItGas4QgDmidlrNkVjDoYgncFQRQqDy3bdQ/ec/yDfo9Uh9cRHihg2XlRlE2qDm\nBQ3PPXWLlQzxnj8LR95WOLfnwrl3D+DxNGo/KT4B5tsH+W/WMDAbuqTkMHfaPGrOEIA5onaxkiNa\nx6GIJ3DUEEKg6ndrULV+nXyDTofUeQsRN/wnAfswiLRBzQsannvqFosZ4quugvOrnf672e3Mg6is\naNyOej1MfW6BJXsozNk5MLRpF95Gm0DNGQIwR9QuFnNEizgU8QSOGpW//w2q3lsrL0oSUue+hLgR\nd9W7D4NIG9S8oOG5p26xniHC44HrwP7a5yFtgff0qUbva+jcFebaj9kZs3pB0unC2Ol1elFxhgDM\nEbWL9RzRCg5FPIGjQtX691D527flRUlCynMvIP6noxvcj0GkDWpe0PDcUzdmyGVCCHiOH617YKz7\n4HeN3ldnTYd58FD/x+xu7Q/JbAljp4HUnCEAc0TtmCPawKGIJ7Diqv68HpVrVgXUU2Y+j/hRY665\nL4NIG9S8oOG5p27MkIZ5Sy7CuWMbHNu2wPn1bsDlbNR+ksUC020D/R+zGzwU+tS0MHeq7gwBmCNq\nxxzRhmBzRJuPxqaIqfrgT/UORMnTnrvuQEREROGjT2+B+NH/hfjR/wWf3Q7X11/5B6Qd2+ArK21w\nP+FwwLntP3Bu+w8gSTDe1AeWwTmwDMmBoUOniPVPRBRJvFJEzVb90QeoeGNpQD35mWeRcP+4Rh2D\n785og5rf5eW5p27MkKYTXi/ch76DY5v/Y3beouON3lffvkPt7b6HwXhjb0h6fUh6UnOGAMwRtWOO\naAM/PscTWBHVn3yEiuWvBtSTJk1F4rgHGn0cBpE2qHlBw3NP3ZghwfOcPAFHXi6ceVvh+m4/4Gvc\n/4+6lFSYB2XDkj0Mpttuhy4+vtk9qDlDAOaI2jFHtIFDEU/giKvZ+DHKl7wcUE96YjISH3ioScdi\nEGmDmhc0PPfUjRkSWr6yMjh2boMzLxfO3Tsh7PbG7Wgywdyvv/9GDYOHQt+iZZN+r5ozBGCOqB1z\nRBs4FPEEjqiaTZ+hfPEC4KrTJvFXE5H04CNNPh6DSBvUvKDhuaduzJDwEU4nnN/sqbubna/kYqP3\nNWb1gnnIMFgG58DQpSskSbrmz6s5QwDmiNoxR7SBQxFP4Iixf74JZa+8EDgQTXgMSQ8/3qxjMoi0\nQc0LGp576sYMiQzh88FdcAjO7blw5G2F50hho/fV39Cm7nlIpj63QDIE3uNJzRkCMEfUjjmiDRyK\neAJHhP2Lz1G28PmAz5onjH8YSb+aeN13ARvCINIGNS9oeO6pGzNEGZ4zp+DM2wrH9ly49u0FvN5G\n7SclJsE8cLD/Y3YDBkOXmAhA3RkCMEfUjjmiDRyKeAKHnT33C5TNnxPwl17Czx9E0pOTmz0QAQwi\nrVDzgobnnroxQ5Tnq6yAc9cO/80aduVBVFc3bkeDAaabb4UlOwcJOcPQsme38DYaRjz/1I05og0c\ningCh5UjbwtK580KHIj+5xdImjQ1qIEIYBBpBYciUgozJLoItxuu/XvhyNsKZ94WeM+dbfS+fQ7m\nh7Gz8OL5p27MEW3gw1spbBw781D6wnMBA1H8feNCMhAREZG2SEYjzLfdDvNtt0P8ejo8Rwprb/ed\nC3fBIaXbIyJqEIciqpdz906UzpsJeDyyevy99yP5mRkciIiI6JokSYKxWw8Yu/VA0v/+Ct7z5+DY\nsQ3ObVvg/GYP4HYr3SIRUR0ORRTAuXc3bHNmAC6XrB43agySp87iQERERE2mz2iFhDFjkTBmLHw1\n1XDu3gXnti1w7MyDqChXuj0iinEcikjGuX8vSmdPA1xOWT1u5CikzJgDSadTqDMiItIKXXwC4oYN\nR9yw4RAeD3yHC5RuiYhiHFe4VMd1YD9KZ02BcDhkdcudI5Eyax4HIiIiCjnJYID5pt5Kt0FEMY6r\nXAIAuL4/ANvMZyDsdlnd8uM7kTp7PiS9XqHOiIiIiIjCi0MRwZV/ELZnJ0PUyJ8tYcn5MVKfX1jv\n08eJiIiIiLSCQ1GMc/9QANv0pwMetmcePBSpL7zCgYiIiIiINI9DUQxzHylEyfRJEFWVsrp5YDbS\nXloMyWhUqDMiIiIiosjhUBSj3MeOwDb1qYDboJr6D0TagtcgmUwKdUZEREREFFkcimKQ58Rx2KY9\nBV95maxu6ncbrK8shWQ2K9QZEREREVHkcSiKMZ7iIpRMnQifzSarm/regrRFr0MyWxTqjIiIiIhI\nGRyKYojnVDFKpkyEr+SirG7s3Rdpi1dCFxenUGdERERERMrhUBQjPGdOwzZ1InwXzsvqxl69YX1t\nJXTx8Qp1RkRERESkLA5FMcB77ixsUybCe+6srG7M7Anr0lXQJSQq1BkRERERkfI4FGmc98J5lEyd\nCO/Z07K6oXsmrMvfgi6RAxERERERxTYORRrmLbmIkikT4T1VLKsbunZH+vK3oEtKVqgzIiIiIqLo\nwaFIo7y2Ev9AVFwkqxs6d4H19dXQpaQq1BkRERERUXThUKRB3rJS2KY9BW/RcVld36ETrK+/DX1q\nmjKNERERERFFIQ5FGuMrL4Nt2iR4jh2V1fXtOiB95TvQW9MV6oyIiIiIKDpxKNIQX2UFSqY/Dc+R\nQlld36Yt0le8DX16C4U6IyIiIiKKXhyKNMJXVQXbjMnwFBbI6vrWbZC+cg30Ga0U6oyIiIiIKLpx\nKNIAX3UVbM/+Gu78g7K6LqMVrCvfgb5Va4U6IyIiIiIKD+HzwVNcBPvnm1Dx/rqgjmUIUU+kEF9N\nDWyzpsB98ICsrmuZgfSVa2C4oY1CnRERERERhYYQAt6zZ+DOPwh3wSG4Cw7C/UM+RFXV5R+aMrnZ\nx+dQpGI+ux2ls6fCfWC/rK5Lb4H0FW/D0LadQp0RERERETWPEAK+ixdkA5Cr4BBEeXnYfieHIpUS\nTgdK50yDa99eWV2XZkX6indgaN9Roc6IiIiIiBrPW2rzDz/5B+sGIZ+tJKI9cChSIeF0wjb3Wbj2\n7pHVdSmpsK54G4aOnZRpjIiIiIjoGnwV5XAX5MOdfxCugtoB6Py5oI6ps1ph6nljUMfgUKQywuVC\n6Quz4Nq9U1aXklNgfX01jJ27KtQZEREREdFlvuoquH8o8H//p/YKkPf0qaCOKaWkwJTZE8bMXjBm\n9YIxsyd0LVrCaNQHdVwORSoi3G6Uzp8N5848WV1KTEL68rdg7NZDoc6IiIiIKJb57HZ4Dv/g//7P\npQGo6ERQx5QSEmC8agDSt74BkiSFqOvLOBSphPB4ULZgLpx5ubK6lJAA67I3YeyRpVBnRERERBRL\nhNMJ99HDl2+EkH8QnhPHAJ+v2ceU4uJg7J5VOwT1hLFnL+jbtIOki8wThDgUqYDweFD28jw4cr+U\n1aX4BFiXvhn0ZyiJiIiIiOojPB54jh7xfwSu4BBc+QfhOXoY8Hqbf1CTGcZuPfzDT1ZPGLN6wdC+\nIyR9cB+BCwaHoignvF6UvTofji83y+pSXBysS96A6cbeCnVGRERERFoivF54ThyrvQ127d3gjhQC\nLlfzD2owwNi1++UrQJk9YejcFZIhusaQ6OqGZITPh/IlC+HY/G/5BrMZaYtXwNS7rzKNEREREZGq\nCZ8P3uKiugHIlX8InsJ8CIej+QfV62Ho1EU2ABm7dodkMoWu8TDhUBSlhM+H8mWLYN+0Ub7BZIZ1\n8QqYb75VmcaIiIiISFWEEPCeOQV3/qHLV4F+OARRXd38g0oS9O07wlR7AwRjVk8Yu2VCslhC13gE\ncSiKQkIIVKxYAvvGj+UbTCZYFy2DuV9/ZRojIiIioqgmhIDvwvna5wBdHoJERXlQx9W3bVd7F7ja\nK0DdM6FLSAxR18rjUBRlhBCoeGMZaj75UL7BaETawiUw9x+oTGNEREREFHW8tpLL3/8pOAR3wUH4\nbLagjqlv1br26k/tVaAeWdAlp4So4+jEoSiKCCFQuXolajZ8IN+g1yPtpcWwDMxWpjEiIiIiUpyv\nvAzuH/L9zwHKrx2ALpwP6pg6a7p/+Lk0AGX2hD7NGqKO1YNDUZQQQqDy3bdQ/bc/yTfo9UidvwiW\n7BxlGiMiIiKiiPNVVcH9Q/4VV4EOwnvmdFDH1KWkym6DbczsBX2LliHqWN04FEUBIQSqfrcG1X/+\ng3yDTofU5xcgLme4Mo0RERERUdj57HZ4CgvgLjjovwpUcAjek0VBHVNKTLx8B7isG/1XgFq1hiRJ\nIepaWzgURYGq93+LqvXr5EVJQuqc+Ygb/hNlmiIiIiKikBNOJ9xHCv0PQ60dgDwnjgM+X7OPKcXF\nwdgjq3YI8n8UTt+mLSSdLnSNaxyHIoVVrX8PVe+tlRclCSnPvYC4EXcp0xQRERERBU243fAcO3L5\nTnD5B+E5dgTwept/UJMZxu49/MNP7c0QDO07QNLrQ9d4DOJQpKCqP69H5W/fDqinPDsX8T8drUBH\nRERERNQcwuOB58Rx/xWgS98DOlIIuN3NP6jBAGPX7rJbYRs6dYFk4BI+1Pj/qEKqPvgTKtesCqgn\nT3sO8aPGKNARERERETWG8PngPVkE16UBqOAQPIUFEA5H8w+q18PQucvlK0CZPWHs0g2SyRS6xqlB\nHIoUUP3RB6hcvSKgnvzMs0gYM1aBjoiIiIioPkIIeE+fuuIK0CG4f8iHqKlu/kElCYYOnWS3wTZ2\n6wHJYgld49QkHIoirPqTj1DxxtKAetKkqUi4f5wCHRERERER4B+AfOfP+a8A5R+quwokKiuCOq6+\nbfvLA1BWTxi7Z0IXnxCirikUOBRFUM3Gj1Gx/NWAetITk5E47gEFOiIiIiKKXd6Si3AX5sN5vBAV\n+/bDlX8IvlJbUMfUt76h7gYIxsyeMPbIgi4pOUQdU7hwKIqQmk2foXzpKwH1xF9NROIDDynQERER\nEVHs8JWVyb4D5C44BN+F80EdU9eipXwAyuwJfWpaiDqmSOJQFAH2zzehfPECQAhZPXHCY0h68BGF\nuiIiIiLSJl9lJdyF+f47wNV+DM579nRQx9SlpF7xETj/v/UtWoaoY1Iah6Iws3+5GWWLXgwYiBLG\nP4zECY8p1BURERGRNvhqauApLIAr//JVIG9xUVDHlBKTLn//J7MXTFm9oMtoBUmSQtQ1RRsORWHk\nyP0SZQufD3hCccLPH0TSrybyDxYRERFREwinA+7Dhf4rQAWH4C44CM+J4wFvPjeFFBeP+JtuhK5b\nJvTdaz8C17Yd12kxhkNRmDjyclH60pyAJxYn/M8vkPTkZP5BIyIiIroG4XbDc/QwXJcehFpwEJ5j\nRwPWVk1iNsPYPbP2+z/+j8BZunSGNT0JpaXV8Hh81z8GaRKHojBw7MxD6YvPAR6PrB5/3zgkTZrK\ngYiIiIjoCsLjgefEMf/3f2oHIPfRw4Db3fyDGo0wdu1+eQDK6glDx86QDPLlr6TTBdk9aQGHohBz\n7t6J0nkzA/4Qx997P5KfmcGBiIiIiGKa8HrhOVlU9/E3d/5BuA//ADidzT+oXg9D5651N0EwZfaE\noXNXSCZT6BonTeNQFELOvbthmzMDcLlk9bhRY5A8dRYHIiIiIoopQgh4TxXLB6AfCiDsNc0/qCTB\n0LFT7R3gau8G1607JLMldI1TzOFQFCLO/XtROnsa4JK/yxE3chRSZszhpVkiIiLSNCEEvOfOXjEA\n+e8EJ6oqgzquvl2Hy3eBy+wJQ/dM6OLjQ9Q1kR+HohBwHdiP0llTIBwOWd1y50ikzJrHgYiIiIg0\nx3vxgmz4cRccgq+sNKhj6lu3ufwcoKyeMHbPgi4pKUQdEzWMQ1GQXN8fgG3mMxB2u6xu+fGdSJ09\nH5Jer1BnRERERKHhLSu94jbYtQPQxQtBHVPXMqP2Jgg9YcrqBWOPntClpoaoY6Km4VAUBFf+Qdie\nnQxRUy2rW3J+jNTnFwbc3YSIiIgo2vkqK2TDj7vgELxnzwR1TF1qWu13gHrWXQnSp7cIUcdEweOq\nvZncPxTANv1piGr5QGQePBSpL7zCgYiIiIiinq+mGu4f8v3DT+3H4LynTgZ1TCkp+Yrhx38VSNey\nFW84RVGNK/dmcB8pRMn0SQFfHDQPzEbaS4shGY0KdUZERERUP+FwwH24QPYdIE/RcUCIZh9Tik+A\nsUdW7Y0Qaq8A3dCWAxCpDoeiJnIfOwLb1KcgKspldVP/gUhb8Brvh09ERESKEy4X3EcPy74H5Dl+\nFPB6m39Qs9k/AF36HlBmL+jbd+ANpUgTOBQ1gefEcdimPQVfeZmsbup3G6yvLIVkNivUGREREcUq\n4fHAc/yo/EYIRwoBj6f5BzUaYezW4/LH4DJ7wdCxE78eQJrFM7uRPMVFKJk6ET6bTVY39b0FaYte\n5wPDiIiIKOyE1wvPyRP+j8BdGoIO/xDwnMQm0eth6NKt9uqP/yNwhs5d+XUAiikcihrBc6oYJVMm\nwldyUVY39u6LtMUroYuLU6gzIiIi0irh88F7ulg+ABXmBzwGpEl0Ohg6doIxs1fdA1GNXbvxzV2K\neRyKrsNz5jRsUyfCd+G8rG7s1RvW11byicpEREQUNCEEvGfP1H787aB/CPohH6KqKqjj6tt3uPwc\noMxeMHTrwbULUT04FF2D99xZ2KZMhPfcWVndmNkT1qWroEtIVKgzIiIiUishBHwXL8gGIFfBIYjy\n8uvvfA36G9r4r/zUfgTO2CMLukSuVYgag0NRA7wXzqNk6kR4z56W1Q3dM2Fd/hZDhoiIiBrFW2qr\nfQ7Qwbp/+2wlQR1T1zKj7iNwpksDUEpqiDomij0ciurhLbmIkikT4T1VLKsbunZH+vK3oEtKVqgz\nIiIiima+inK4C/L9V4AKDsGVfxC+8+eCOqYuzeq/8nPFFSB9eosQdUxEAIeiAF5biX8gKi6S1Q2d\nu8D6+mq+C0NERER1qr7ahYrde+E85B+Crn5Dtamk5JQrngPkH4J0LTP4MFSiMONQdAVvWSls056C\nt+i4rK7v0AnW19+GPjVNmcaIiIgoKh2d8L/N3ldKSICxR8/LzwLq2Qv61m04ABEpgENRLV95GWzT\nJsFz7Kisrm/XAekr34Hemq5QZ0RERKR2ksUCQ/csmLIuD0H6dh0g6XRKt0ZE4FAEAPBVVqBk+tPw\nHCmU1fVt2iJ9xdv83C4RERE1nskEY9ful78HlNkTho6dIen1SndGRA2I+aHIV1UF24zJ8BQWyOr6\n1m2QvnIN9BmtFOqMiIiIop7BAGOXrpdvhZ3ZC4bOXSAZjUp3RkRNENNDka+6CrZnfw13/kFZXZfR\nCtaV70DfqrVCnREREZEa3LRnL8qr3fB4fEq3QkRBiNkPsvpqamCbNQXugwdkdV3LDKSvXAPDDW0U\n6oyIiIjUQmcyKd0CEYVATA5FPrsdpbOnwn1gv6yuS2+B9BVvw9C2nUKdERERERFRpMXcUCScDpTO\nmQbXvr2yui7NivQV78DQvqNCnRERERERkRJiaigSTidsc5+Fa+8eWV2Xkgrrirdh6NhJmcaIiIiI\niEgxMTMUCZcLpS/Mgmv3TlldSk6B9fXVMHbuqlBnRERERESkpJgYioTbjdL5s+HcmSerS4lJSF/+\nFozdeijUGRERERERKU3zQ5HweFC2YC6cebmyupSQAOuyN2HskaVQZ0REREREFA00PRQJjwdlL8+D\nI/dLWV2KT4B16Zsw9bxRoc6IiIiIiChaaHYoEl4vyl6dD8eXm2V1KS4O1iVvwHRjb4U6IyIiIiKi\naKLJoUj4fChfshCOzf+WbzCbkbZ4BUy9+yrTGBERERERRR3NDUXC50P5skWwb9oo32Ayw7p4Bcw3\n36pMY0REREREFJUUGYrKysqwcOFCDB8+HH379sWYMWPw4YcfBn1cIQQqViyBfePH8g0mE6yLlsHc\nr3/Qv4OIokO4coSIYgMzhIiuZIj0L7Tb7XjkkUdQWFiI8ePHo3PnzvjXv/6FuXPnoqSkBI8//niz\njs6Bn/EAAAhKSURBVCuEQMUby1DzyVWBZjQibeESmPsPDEH3RBQNwpUjRBQbmCFEdLWID0Xr16/H\noUOHsHz5ctx9990AgHHjxuHRRx/FW2+9hTFjxqBVq1ZNOqYQApWrV6JmwwfyDXo90l5aDMvA7FC1\nT0RRIBw5QkSxgxlCRFeL+MfnPv74Y7Rs2bIuhC559NFH4XK58OmnnzbpeEIIVL77Fqr/9if5Br0e\nqfMXwZKdE2zLRBRlQp0jRBRbmCFEdLWIDkVVVVU4evQo+vTpE7DtUu3bb79t9PGEEKj4zTuo/vMf\n5Bt0OqQ+vxBxOcOD6peIok+oc4SIYgszhIjqE9Gh6Ny5cxBCoHXr1gHbEhMTkZCQgOLi4kYf7/zb\nq1Hx/u/kRZ0OqXNeQtzwEcG2S0RRKNQ5QkSxhRlCRPWJ6FBUWVkJAEhISKh3e1xcHGpqahp9vHOr\n35IXJAkps15A3IifNrtHIopuoc4RIootzBAiqk9EhyIhxHW36/X6Zh8/5dnnEf/TUc3en4iiX7hz\nhIi0jRlCRPWJ6N3nLr0rY7fb691ut9vRvn37Zh077dk5SBzzX83ujZSh1+tk/yZ1iuTrF+oc4bmn\nbswQbVBzhgA8/9SOOaINwb5+ER2K2rVrB0mScPbs2YBtVVVVqKmpqfczvg3pczA/lO2RgpKT45Ru\ngVQi1DnCc08b+DpSY4U6QwCef1rB1zG2RXQkjo+PR9euXfHdd98FbNu3bx8AoF+/fpFsiYhUhjlC\nRMFghhBRfSJ+nfDee+/FmTNn8M9//rOuJoTAunXrYDabA54ZQER0NeYIEQWDGUJEV5PE9b5xGGJO\npxNjx45FUVERxo8fj86dO2Pjxo3YtWsXZs2ahQkTJkSyHSJSIeYIEQWDGUJEV4v4UAQApaWlWLFi\nBb744gtUV1ejc+fOePjhh3HPPfdEuhUiUinmCBEFgxlCRFdSZCgiIiIiIiKKFrz3IBERERERxTQO\nRUREREREFNM4FBERERERUUzjUERERERERDFNdUNRWVkZFi5ciOHDh6Nv374YM2YMPvzwQ6XboqsE\n8zpt2LABWVlZ9f4ze/bsMHdOzbF//3706tULO3bsULqVRmGORD9mSOxRU44wQ9SBORJbgs0QQ4j7\nCSu73Y5HHnkEhYWFdc8V+Ne//oW5c+eipKQEjz/+uNItEoJ/nQoKCiBJEhYtWgSDQX6KdujQIZyt\nUzMcP34ckyZNglpuZMkciX7MkNijphxhhqgDcyS2hCRDhIq8++67IisrS2zcuFFWf+SRR0Tv3r3F\n2bNnFeqMrhTs6/S///u/IicnJ5wtUoj8v//3/8SAAQNEVlaWyMrKEtu3b1e6petijkQ/ZkhsUVuO\nMEPUgTkSO0KVIar6+NzHH3+Mli1b4u6775bVH330UbhcLnz66acKdUZXCvZ1KigoQPfu3cPZIoXA\n448/jsmTJyMjIwOjRo1Sup1GY45EP2ZI7FBjjjBD1IE5EhtCmSGqGYqqqqpw9OhR9OnTJ2Dbpdq3\n334b6bboKsG+TufPn0dpaWldELndbrhcrvA0S0E5fvw4pk+fjo8++gidOnVSup1GYY5EP2ZIbFFb\njjBD1IE5EjtCmSGq+U7RuXPnIIRA69atA7YlJiYiISEBxcXFCnRGVwr2dcrPzwcAFBcX4/7770dB\nQQF8Ph9uuukmTJs2DYMGDQpb79Q0GzduhNFoVLqNJmGORD9mSGxRW44wQ9SBORI7QpkhqrlSVFlZ\nCQBISEiod3tcXBxqamoi2RLVI9jXqaCgAADwzTffYPTo0Vi9ejVmzpyJM2fO4NFHH8XmzZtD3zQ1\ni5oWMpcwR6IfMyS2qC1HmCHqwByJHaHMENVcKRLXuZuEEAJ6vT5C3VBDgn2dbr75ZkycOBFjx45F\nu3btAAA/+tGPMHLkSIwePRoLFizAHXfcAUmSQto3xQbmSPRjhlA0Y4aoA3OEmkM1V4ouTft2u73e\n7Xa7HUlJSZFsieoR7OvUv39/PPPMM3UhdEmbNm0wYsQIXLhwoe4dHKKmYo5EP2YIRTNmiDowR6g5\nVDMU/f927tA1tTAO4/gjVxhYz8QFZYjhFJPBtjw22IzGVYtVjaaT/BvMik1QTMIw6YrhwBBNFk8U\n1BWDC/dy4V4vu9vc5jl7v5943vI7/OSBBzxvPB5XKBSS53l7Z+v1Wk9PT//87yi+1mfuybIsSdJm\nszloRpiLHPE/MgR+RoYEAzmC9whMKYpEIkqlUnJdd+9sPB5LkjKZzFePhb8cuqdCoaDLy0ttt9u9\ns9lsJkk6Pz//oGlhGnLE/8gQ+BkZEgzkCN4jMKVIkm5vb7VYLNTtdn8/2+12qtfrOjk52buLHsdx\nyJ6i0ajm87lardYfz4fDoQaDgS4uLnR6evpps+P7I0f8jwyBn5EhwUCO4K0Cc9GCJN3d3andbqtS\nqch1XSWTSXU6HQ2HQ5XLZX6gPvHaPU0mE00mE9m2Ldu2JUnFYlGDwUCO4+jx8VHpdFrT6VTNZlNn\nZ2eqVqtHfDN8B+SI/5Eh8DMyJBjIEbzVj2qANhsOh3V1daXlcqler6d+v69IJKJSqaR8Pn/s8fDL\na/fUaDTkOI4sy1I2m5X08+PIm5sbrVYr3d/fq9fryfM8XV9fq1arKRaLHeu18ILRaKSHhwflcjkl\nEoljj/MicsT/yBAzBSVHyJBgIEfMc2iGhHb/u7cQAAAAAL6xQH1TBAAAAAAfjVIEAAAAwGiUIgAA\nAABGoxQBAAAAMBqlCAAAAIDRKEUAAAAAjEYpAgAAAGA0ShEAAAAAo1GKAAAAABiNUgQAAADAaJQi\nAAAAAEajFAEAAAAwGqUIAAAAgNGeAYDPfC+8vsg9AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11c840f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "make_linear_trio()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def make_stairs():\n",
    "    plt.figure(figsize=(6,6))\n",
    "    for i in range(5):\n",
    "        plt.plot([i*.2, (i+1)*.2], [i*.2, i*.2], lw=2, color=af_clr)\n",
    "        plt.scatter(i*.2, i*.2, s=100, facecolor=af_clr, edgecolor='none')\n",
    "        plt.scatter((i*.2)+.2, i*.2, s=100, lw=2, facecolor='white', edgecolor=af_clr, zorder=10)\n",
    "    plt.scatter(1, 1, s=100, facecolor=af_clr, edgecolor='none', zorder=20)\n",
    "    plt.xlim(-.05, 1.05)\n",
    "    plt.ylim(-.05, 1.05)\n",
    "    file_helper.save_figure('stairs')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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eNp6901nqcOkv5P3XdvlPFhn3sUXHqNNd9yh67K/PcHWtT8T5veT5+1uSz6eKvDyd/Nsm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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11d3cc320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "make_stairs()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def make_steps():\n",
    "    plt.figure(figsize=(8, 4))\n",
    "    plt.subplot(1, 2, 1)\n",
    "    plt.plot([-2, 0], [-1, -1], lw=2, color=af_clr)\n",
    "    plt.plot([0, 2], [1, 1], lw=2, color=af_clr)\n",
    "    plt.scatter(0, -1, facecolor='white', edgecolor=af_clr, s=100, lw=3, zorder=10)\n",
    "    plt.scatter(0, 1, facecolor=af_clr, edgecolor='none', s=100, lw=3, zorder=10)\n",
    "    plt.plot([-2, 2], [0,0], color='black', lw=1)\n",
    "    plt.plot([0,0,], [-5,5], color='black', lw=1)\n",
    "    plt.xlim(-2, 2)\n",
    "    plt.ylim(-2.5, 2.5)\n",
    "    plt.xticks([0], ['threshold'])\n",
    "    plt.yticks([0], [0])\n",
    "    plt.title('(a)')\n",
    "    \n",
    "    plt.subplot(1, 2, 2)\n",
    "    plt.plot([-2, 0], [-1, -1], lw=3, color=af_clr, zorder=10)\n",
    "    plt.plot([0, 2], [1, 1], lw=3, color=af_clr, zorder=10)\n",
    "    plt.plot([0, 0,], [-1, 1], lw=3, color=af_clr, zorder=10)\n",
    "    plt.plot([-2, 2], [0,0], color='black', lw=1)\n",
    "    plt.plot([0,0,], [-5,5], color='black', lw=1)\n",
    "    plt.xlim(-2, 2)\n",
    "    plt.ylim(-2.5, 2.5)\n",
    "    plt.xticks([0], ['threshold'])\n",
    "    plt.yticks([0], [0])\n",
    "    plt.title('(b)')\n",
    "    file_helper.save_figure('steps-1')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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KewAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11eb3c198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "make_steps()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def make_unit_steps():\n",
    "    plt.figure(figsize=(8, 4))\n",
    "    plt.subplot(1, 2, 1)\n",
    "    plt.plot([-1, 0], [0, 0], lw=3, color=af_clr, zorder=10)\n",
    "    plt.plot([0, 1], [1, 1], lw=3, color=af_clr, zorder=10)\n",
    "    plt.scatter(0, 0, facecolor='white', edgecolor=af_clr, s=100, lw=3, zorder=20)\n",
    "    plt.scatter(0, 1, facecolor=af_clr, edgecolor='none', s=100, lw=3, zorder=20)\n",
    "    plt.plot([-2, 2], [0,0], color='black', lw=1)\n",
    "    plt.plot([0,0,], [-5,5], color='black', lw=1)\n",
    "    plt.xlim(-1, 1)\n",
    "    plt.ylim(-1.5, 1.5)\n",
    "    plt.xticks([0], ['threshold'])\n",
    "    plt.yticks([-1,0,1],[-1,0,1])\n",
    "    plt.title('unit step')\n",
    "    \n",
    "    plt.subplot(1, 2, 2)\n",
    "    plt.plot([-1, 0], [0, 0], lw=3, color=af_clr, zorder=10)\n",
    "    plt.plot([0, 1], [1, 1], lw=3, color=af_clr, zorder=10)\n",
    "    plt.scatter(0, 0, facecolor='white', edgecolor=af_clr, s=100, lw=3, zorder=20)\n",
    "    plt.scatter(0, 1, facecolor=af_clr, edgecolor='none', s=100, lw=3, zorder=20)\n",
    "    plt.plot([-2, 2], [0,0], color='black', lw=1)\n",
    "    plt.plot([0,0,], [-5,5], color='black', lw=1)\n",
    "    plt.xlim(-1, 1)\n",
    "    plt.ylim(-1.5, 1.5)\n",
    "    plt.xticks([0], [0])\n",
    "    plt.yticks([-1,0,1],[-1,0,1])\n",
    "    plt.title('Heaviside step')\n",
    "    file_helper.save_figure('unit-steps')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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v9da9PIdm9erVqlChgtq0aeNxnlKbNm0UGRmpt99+W7/88ouioqJ09uxZLVy4UBcuXHCb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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ed73208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "make_unit_steps()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def make_sign_steps():\n",
    "    plt.figure(figsize=(8, 4))\n",
    "    \n",
    "    plt.subplot(1, 2, 1)\n",
    "    plt.plot([-1, 0], [-1, -1], lw=3, color=af_clr, zorder=10)\n",
    "    plt.plot([0, 1], [1, 1], lw=3, color=af_clr, zorder=10)\n",
    "    plt.scatter(0, -1, facecolor='white', edgecolor=af_clr, s=100, lw=3, zorder=20)\n",
    "    plt.scatter(0, 1, facecolor=af_clr, edgecolor='none', s=100, lw=3, zorder=20)\n",
    "    plt.plot([-2, 2], [0,0], color='black', lw=1)\n",
    "    plt.plot([0,0,], [-5,5], color='black', lw=1)\n",
    "    plt.xlim(-1, 1)\n",
    "    plt.ylim(-1.5, 1.5)\n",
    "    plt.xticks([0], [0])\n",
    "    plt.yticks([-1,0,1],[-1,0,1])\n",
    "    plt.title('sign type 1')\n",
    "    \n",
    "    plt.subplot(1, 2, 2)\n",
    "    plt.plot([-1, 0], [-1, -1], lw=3, color=af_clr, zorder=10)\n",
    "    plt.plot([0, 1], [1, 1], lw=3, color=af_clr, zorder=10)\n",
    "    plt.scatter(0, -1, facecolor='white', edgecolor=af_clr, s=100, lw=3, zorder=20)\n",
    "    plt.scatter(0, 1, facecolor='white', edgecolor=af_clr, s=100, lw=3, zorder=20)\n",
    "    plt.scatter(0, 0, facecolor=af_clr, edgecolor='none', s=100, lw=3, zorder=20)\n",
    "    plt.plot([-2, 2], [0,0], color='black', lw=1)\n",
    "    plt.plot([0,0,], [-5,5], color='black', lw=1)\n",
    "    plt.xlim(-1, 1)\n",
    "    plt.ylim(-1.5, 1.5)\n",
    "    plt.xticks([0], [0])\n",
    "    plt.yticks([-1,0,1],[-1,0,1])\n",
    "    plt.title('sign type 2')\n",
    "    file_helper.save_figure('sign-steps')\n",
    "    \n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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tfe+TsyzevHFm1FZUpB8M8sgeJZXt8+c1eEazy4iRceiDv41+9/46Pva92dHv3l/HoQ/+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\nGbEJAEAy/w+T+7kznD5O5wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11f0604a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "make_sign_steps()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def make_piecewise_linears():\n",
    "    def set_common_elements(limit):\n",
    "        plt.plot([-limit, limit], [0,0], color='black', lw=1)\n",
    "        plt.plot([0,0,], [-limit,limit], color='black', lw=1)\n",
    "        plt.xticks([-limit, -limit/2, 0, limit/2, limit],[-limit, '', 0, '', limit])\n",
    "        plt.yticks([-limit, -limit/2, 0, limit/2, limit],[-limit, '', 0, '', limit])\n",
    "        plt.xlim(-limit, limit)\n",
    "        plt.ylim(-limit, limit)\n",
    "    \n",
    "    plt.figure(figsize=(6,6))\n",
    "    plt.plot([-5, 0], [0, 0], lw=3, color=af_clr, zorder=10)\n",
    "    plt.plot([0, 5], [0, 5], lw=3, color=af_clr, zorder=10)\n",
    "    set_common_elements(5)\n",
    "    plt.title('ReLU')\n",
    "    file_helper.save_figure('ReLU')\n",
    "    plt.show()\n",
    "    \n",
    "    plt.figure(figsize=(6,6))\n",
    "    plt.plot([-5, 0], [-1, 0], lw=3, color=af_clr, zorder=10)\n",
    "    plt.plot([0, 5], [0, 5], lw=3, color=af_clr, zorder=10)\n",
    "    set_common_elements(5)\n",
    "    plt.title('Leaky ReLU')\n",
    "    file_helper.save_figure('Leaky-ReLU')\n",
    "    plt.show()\n",
    "    \n",
    "    plt.figure(figsize=(6,6))\n",
    "    plt.plot([-5, -1], [-1, -1], lw=3, color=af_clr, zorder=10)\n",
    "    plt.plot([-1, 5], [-1, 5], lw=3, color=af_clr, zorder=10)\n",
    "    set_common_elements(5)\n",
    "    plt.title('Shifted ReLU')\n",
    "    file_helper.save_figure('Shifted-ReLU')\n",
    "    plt.show()    \n",
    "    \n",
    "    plt.figure(figsize=(6,6))\n",
    "    xs = np.linspace(-5, 5, 100)\n",
    "    ys = [x if x>0 else (math.exp(x)-1) for x in xs]\n",
    "    plt.plot(xs, ys, lw=3, color=af_clr, zorder=10)\n",
    "    set_common_elements(5)\n",
    "    plt.title('ELU')\n",
    "    file_helper.save_figure('Exponential-ReLU')\n",
    "    plt.show()    \n",
    "    \n",
    "    plt.figure(figsize=(10,3))\n",
    "    plt.subplot(1, 3, 1)\n",
    "    plt.plot([-1, 0], [-.1, 0], lw=3, color=af_clr, zorder=10)\n",
    "    plt.plot([0, 1], [0, 1], lw=3, color=af_clr, zorder=10)\n",
    "    plt.title(\"factor 0.1\")\n",
    "    set_common_elements(1)\n",
    "    plt.subplot(1, 3, 2)\n",
    "    plt.plot([-1, 0], [-.3, 0], lw=3, color=af_clr, zorder=10)\n",
    "    plt.plot([0, 1], [0, 1], lw=3, color=af_clr, zorder=10)\n",
    "    plt.title(\"factor 0.3\")\n",
    "    set_common_elements(1)\n",
    "    plt.subplot(1, 3, 3)\n",
    "    plt.plot([-1, 0], [-.7, 0], lw=3, color=af_clr, zorder=10)\n",
    "    plt.plot([0, 1], [0, 1], lw=3, color=af_clr, zorder=10)\n",
    "    plt.title(\"factor 0.7\")\n",
    "    set_common_elements(1)\n",
    "    file_helper.save_figure('Parametric-ReLU')\n",
    "    plt.show()\n",
    "    \n",
    "    \n",
    "    plt.figure(figsize=(10,3))\n",
    "    plt.subplot(1, 3, 1)\n",
    "    plt.plot([-1, 1], [0, 0], lw=2, color='#8C4A56', zorder=20)\n",
    "    plt.plot([-1, 1], [-1, 1], lw=2, color='#5679A6', zorder=20)\n",
    "    plt.plot([-1, 0], [0, 0], lw=4, color=af_clr, zorder=10)\n",
    "    plt.plot([0, 1], [0, 1], lw=4, color=af_clr, zorder=10)\n",
    "    plt.title('(a)')\n",
    "    set_common_elements(1)\n",
    "    \n",
    "    plt.subplot(1, 3, 2)\n",
    "    plt.plot([-1, -.8], [.6, -1.4], lw=2, color='#8C4A56', zorder=20)\n",
    "    plt.plot([-2, 1.6], [-.2, -.8], lw=2, color='#5679A6', zorder=20)\n",
    "    plt.plot([-.2, 1], [-1, -.2], lw=2, color='#314259', zorder=10)\n",
    "    plt.plot([-1, -.9],[.6, -.38], lw=4, color=af_clr, zorder=10)\n",
    "    plt.plot([-.9, .4],[-.38, -.6], lw=4, color=af_clr, zorder=10)\n",
    "    plt.plot([.4, 1],[-.6, -.2], lw=4, color=af_clr, zorder=10)\n",
    "    plt.title('(b)')\n",
    "    set_common_elements(1)  \n",
    "    \n",
    "    plt.subplot(1, 3, 3)\n",
    "    plt.plot([-1, -.2], [1, -1], lw=2, color='#8C4A56', zorder=20)\n",
    "    plt.plot([ 1,  .2], [1, -1], lw=2, color='#5679A6', zorder=20)\n",
    "    plt.plot([-1,  .4], [.4, -1], lw=2, color='#314259', zorder=20)\n",
    "    plt.plot([ 1, -.4], [.4, -1], lw=2, color='#A3AFBF', zorder=20)\n",
    "    plt.plot([-1, 1], [-.4, -.4], lw=2, color='#6FB5BD', zorder=20)\n",
    "    plt.plot([-1, -.6], [1, 0], lw=4, color=af_clr, zorder=10)\n",
    "    plt.plot([-.6, -.2], [0, -.4], lw=4, color=af_clr, zorder=10)\n",
    "    plt.plot([-.2, .2], [-.4, -.4], lw=4, color=af_clr, zorder=10)\n",
    "    plt.plot([.2, .6], [-.4, 0], lw=4, color=af_clr, zorder=10)\n",
    "    plt.plot([.6, 1], [0, 1], lw=4, color=af_clr, zorder=10)\n",
    "    plt.title('(c)')\n",
    "    set_common_elements(1)\n",
    "    file_helper.save_figure('maxout')\n",
    "    plt.show()\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11f0010f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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gagmC0hIFAFQlQVB6ogCAqiMIOocoAKCqCILOIwoAqBqCoHOJAgCqgiDofKIAgIonCLqG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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11f05b8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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kOeWUU7L77ru3mzdo0KCiNgMA9JDComDBggVpaGjIUUcdlZEjRxa1WgCglxR2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\nKBMFAECS5P8DjJCQn1FoPbwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11d3c2828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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AAKgQBQBAElEAAFSIAgAgiSgAACpEAQCQRBQAABWiAABIIgoAgApRAAAkEQUA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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11c904278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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HJ/UQSSpdvkwFkyZE1FvdO0TxV9/oiHNsDM56AyPQCEqXLlHhzKkR9YzBw5R9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\nSi4ujrgty8WoC30ERjisqq+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hBwAAwMaCW7cof8IYBb/+MuKYOz1D6Q+NVkKPPhYkA6zH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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11f31ef28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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pUZaL9akXiBp8nsqRtk4unR6lpga/w6F2KEKIVsg0cSpGv4/UmsBMjltnoMQc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\nEZEiMewQEREREZEi/T88xSNwdE3KyAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11c87bc88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "make_piecewise_linears()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def make_smooths():\n",
    "    plt.figure(figsize=(6,6))\n",
    "    psize = 8\n",
    "    #plt.plot([-psize, psize], [0, 0], lw=4, color='#8C4A56', zorder=20)\n",
    "    #plt.plot([-psize, psize], [-psize, psize], lw=3, color='#5679A6', zorder=20)\n",
    "    x = np.linspace(-psize, psize, 100)\n",
    "    y = np.log(1+(np.e**x))\n",
    "    plt.plot(x, y, lw=3, color=af_clr, zorder=10)\n",
    "    plt.plot([-psize, psize], [0,0], color='black', lw=1)\n",
    "    plt.plot([0,0,], [-psize, psize], color='black', lw=1)\n",
    "    plt.xticks([-psize,-psize/2, 0, psize/2, psize],[-psize, '', 0, '', psize])\n",
    "    plt.yticks([-psize,-psize/2, 0, psize/2, psize],[-psize, '', 0, '', psize])\n",
    "    plt.xlim(-psize, psize)\n",
    "    plt.ylim(-psize, psize)\n",
    "    plt.title('softplus')\n",
    "    file_helper.save_figure('softplus')\n",
    "    plt.show()\n",
    "    \n",
    "    \n",
    "    plt.figure(figsize=(6,6))\n",
    "    psize = 8\n",
    "    x = np.linspace(-psize, psize, 100)\n",
    "    y = 1/(1+(np.e**-x))\n",
    "    plt.plot(x, y, lw=3, color=af_clr, zorder=10)\n",
    "    plt.plot([-psize, psize], [0,0], color='black', lw=1)\n",
    "    plt.plot([0,0,], [-psize, psize], color='black', lw=1)\n",
    "    plt.xticks([-psize,-psize/2, 0, psize/2, psize],[-psize, '', 0, '', psize])\n",
    "    plt.yticks([0, .25, .5, .75, 1],[0, '', .5, '', 1])\n",
    "    plt.xlim(-psize, psize)\n",
    "    plt.ylim(-.01, 1.01)\n",
    "    plt.title('sigmoid')\n",
    "    file_helper.save_figure('sigmoid')\n",
    "    plt.show()\n",
    "    \n",
    "    \n",
    "    plt.figure(figsize=(6,6))\n",
    "    psize = 8\n",
    "    x = np.linspace(-psize, psize, 100)\n",
    "    y = np.tanh(x)\n",
    "    plt.plot(x, y, lw=3, color=af_clr, zorder=10)\n",
    "    plt.plot([-psize, psize], [0,0], color='black', lw=1)\n",
    "    plt.plot([0,0,], [-psize, psize], color='black', lw=1)\n",
    "    plt.xticks([-psize,-psize/2, 0, psize/2, psize],[-psize, '', 0, '', psize])\n",
    "    plt.yticks([-1, -.5, 0, .5, 1],[-1, '', 0, '', 1])\n",
    "    plt.xlim(-psize, psize)\n",
    "    plt.ylim(-1.01, 1.01)\n",
    "    plt.title('tanh')\n",
    "    file_helper.save_figure('tanh')\n",
    "    plt.show()\n",
    "    \n",
    "    \n",
    "    plt.figure(figsize=(6,6))\n",
    "    psize = 8\n",
    "    x = np.linspace(-psize, psize, 100)\n",
    "    y = 1/(1+(np.e**-x))\n",
    "    plt.plot(x, y, lw=4, color='#F28F38', zorder=10, label='sigmoid')\n",
    "    y = np.tanh(x)\n",
    "    plt.plot(x, y, lw=4, color='#46C9BB', zorder=10, label='tanh')\n",
    "    plt.plot([-psize, psize], [0,0], color='black', lw=1)\n",
    "    plt.plot([0,0,], [-psize, psize], color='black', lw=1)\n",
    "    plt.xticks([-psize,-psize/2, 0, psize/2, psize],[-psize, '', 0, '', psize])\n",
    "    plt.yticks([-1, -.5, 0, .5, 1],[-1, '', 0, '', 1])\n",
    "    plt.xlim(-psize, psize)\n",
    "    plt.ylim(-1.01, 1.01)\n",
    "    plt.title('sigmoid and tanh')\n",
    "    plt.legend(loc='lower right')\n",
    "    file_helper.save_figure('sigmoid-tanh')\n",
    "    plt.show()\n",
    "    \n",
    "\n",
    "    plt.figure(figsize=(6,6))\n",
    "    psize = 8\n",
    "    x = np.linspace(-psize, psize, 100)\n",
    "    y = x/(1+(np.e**-x))\n",
    "    plt.plot(x, y, lw=3, color=af_clr, zorder=10)\n",
    "    plt.plot([-psize, psize], [0,0], color='black', lw=1)\n",
    "    plt.plot([0,0,], [-psize, psize], color='black', lw=1)\n",
    "    plt.xticks([-psize,-psize/2, 0, psize/2, psize],[-psize, '', 0, '', psize])\n",
    "    plt.yticks([-psize,-psize/2, 0, psize/2, psize],[-psize, '', 0, '', psize])\n",
    "    plt.xlim(-psize, psize)\n",
    "    plt.ylim(-psize, psize)\n",
    "    plt.title('swish')\n",
    "    file_helper.save_figure('swish')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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rZT9cwUMGXS7mHoIQIQoAAGGv9NtNyh79gIySkoD1uC4Xl91DEBNj0mTRhSgAAIS10m++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\nAH5EAQAAkEQUAAAAP6IAAABIkv4/S8rSRcmPqw0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11fa010b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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IV5QHAElnV+xUfO1qx4z9HYD0QXkAkHSRxQslY/YNgkEuwQ2kEcoDgKSL1tlk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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11fac0208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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UADAuuyYvFHDqADCCUADAKD+bVeYvfw7UymYzyRAwgVAAwKjs+jelTHegVvaekwx1AyQb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\nYao4+zxVnH+hyk89ndMEAGK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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11fc60ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ylHM8AVFkMBQQUb/Td70FrbbEUb4te4LyfK5kSBQZDAVE1L/MJhhfPqs89NXQ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\niIiIAAD/D0l8YXbPwSHTAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x105ccf0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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fb9oP+HwKPDpV/rO6ObNYnCMKAAAJxTJNFU2frPIlr9sPeL3Kfvhx+c/u7sxiDQBRAABI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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ed06518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "make_smooths()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def softmax(vals):\n",
    "    vsum = np.sum([math.exp(v) for v in vals])\n",
    "    newvals = [math.exp(v)/vsum for v in vals]\n",
    "    return newvals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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GhgwZEtaWlpam1NRUHTx4sMfbe+ihh9Ta2qq77rrLShkA4ClkIwCYIx8BxBtLE+yGhgZJ\nUmpqqml7cnKy6R+iMFNbW6vy8nJ97nOfM/1UEwBiBdkIAObIRwDxxtIfOTMMo9v2nv6hiaefflqt\nra269dZbrZTQid/vk9/v6/X60RII+Dv96yXRrM3t5xsI+JWQEJ0a4vWY9oVX64oGsrHvYnG8UHPP\n+/OSaL5WnNnP6f/GK/LRvbFgV79O1G3XeRnr+7qlpUWVlW/2+PF+v09paeeosfGk2tq6PtfajR17\niRITE3tboiR38y0WstXSBLv908dQKGTaHgqFNGLEiB5t64UXXtCAAQN0xRVXWCmhkwEDUuXzefdN\nZHp6stslRBSN2tLTk6VDtm/WUv8ZGeafkNvZh1d5tTav1mUnstE+sTheqNn9fqxw4rXizP7iGfn4\nT26Nhb7260Tddp+Xsbqv9+zZr6/dtkRKOdemis7Q/KFeffJBTZw40ZbNuZlvXs5WSxPs4cOHy+fz\nqa6uLqytsbFRzc3Npr+xOdM777yjv/3tb7r55pv7FHLHjjV58luaQMCv9PRkBYMhtba2uV1OJ9Gs\nLRg0f/F0SjAY0vHjTVHZdrwe077wal3t7HwhJxv7zuvjxQw1d8/t1wUz0XytOF0sjo925KO93BoL\ndvXrxHls13l5VuzrlHOl/pk2VhfeR1/3tZv55mbfPc1GSxPslJQUjRo1SpWVlWFte/fulSRNmDCh\n2+3s3r1bPp9PX/ziF610H6atzejx5RBuaG1t06lT3nxRjUZtbr+BcGJ/x9sxtYNX67IT2WifWBwv\n1Nx1P17j9PGKxfFhJ/Lxn9waC33t14nz2O59w77uug+79o2b+eblbLV88fqMGTNUW1urbdu2dSwz\nDENr165VUlJS2D0OzbSHLH+gAsDZgmwEAHPkI4B4YukbbEmaN2+eSktLtWTJElVWVionJ0dlZWXa\nvXu3CgsLlZn5ySUN1dXVqq6uVm5urnJzcztto6amRomJiRo4cKA9zwIAXEY2AoA58hFAPLE8wU5K\nSlJJSYmKi4tVWlqqpqYm5eTkaMWKFZo+fXrH48rLy7VmzRotWrQoLCSPHz+u9PT0vlcPAB5BNgKA\nOfIRQDyxPMGWpIyMDBUVFamoqCjiYwoKClRQUGDa9sILL/SmWwDwNLIRAMyRjwDihXdvIAYAAAAA\nQAxhgg0AAAAAgA2YYAMAAAAAYAMm2AAAAAAA2IAJNgAAAAAANujVBPvEiRNavny5Jk+erPHjxysv\nL08bNmzo8fovv/yybrnlFl122WX63Oc+p/z8fL355pu9KQUAPINsBIBwZCOAeGJ5gh0KhbRgwQI9\n88wzuuaaa7R06VINGDBAS5cu1SOPPNLt+s8++6wWLlyohoYG/du//Zvy8/NVXV2tOXPmaN++fb16\nEgDgNrIRAMKRjQDijeX7YJeUlKiqqkorV67UtGnTJEmzZ89Wfn6+Vq9erby8PA0ePNh03SNHjuj+\n++/XJZdcopKSEiUlJUmSpk6dqmnTpunBBx/sUdgCgNeQjQAQjmwEEG8sf4O9ZcsWZWVldYRku/z8\nfLW0tGjr1q0R1920aZNOnjypu+++uyMkJen888/XPffcoy984QtWywEATyAbASAc2Qgg3lj6Brux\nsVE1NTWaMmVKWNu4ceMkSRUVFRHXf/XVV5WamqrLLrtMktTa2qqPP/5Y55xzjm6++WYrpQCAZ5CN\nABCObAQQjyx9g33kyBEZhqEhQ4aEtaWlpSk1NVUHDx6MuP4777yj7Oxs/fWvf9WCBQs0btw4XXrp\npZo+fbp+//vfW68eADyAbASAcGQjgHhkaYLd0NAgSUpNTTVtT05OVnNzc8T1g8GgPvzwQ918883K\nyspScXGxli1bpubmZv3gBz/Qiy++aKUcAPAEshEAwpGNAOKRpUvEDcPotj0QCERsb2lp0QcffKD5\n8+ersLCwY/mUKVM0depU/fSnPzW9jAgAvIxsBIBwZCOAeGRpgt3+CWQoFDJtD4VCGjFiRMT1k5OT\n1dTUpG9/+9udlmdlZemrX/2qysrKVFNTowsvvLBH9fj9Pvn9vh5W75xAwN/pXy+JZm1uP99AwK+E\nhOjUEK/HtKWlRZWVvbvXqN/vU1raOWpsPKm2tq7fZEUyduwlSkxM7NW6TiIb+87L51gk1Nzz/rwk\nmq8VZ/Zz+r/xyGvZKLmTj26NBbv6daJuu85L9nXP+ujrvnYz32IhWy1NsIcPHy6fz6e6urqwtsbG\nRjU3N5v+zqZddna23n77bWVmZoa1tS9rbGzscT0DBqTK5/Pum8j09GS3S4goGrWlpydLh2zfrKX+\nMzLML0Ozsw+vikZte/bs15MvP6KhF2bbvu3uHK6p1W3pd2jixImO920V2WgfL59jkVCz+/1Y4cRr\nxZn9xSuvZaPkbj66NRb62q8Tddt9XrKvu+7Drn3tZr55OVstTbBTUlI0atQoVVZWhrXt3btXkjRh\nwoSI648fP15vv/22qqurdemll3Zqe++99+Tz+TRs2LAe13PsWJMnv6UJBPxKT09WMBhSa2ub2+V0\nEs3agkHzT6idEgyGdPx4U1S2Hc/HdOiF2cq5+AJbt2ul/2gdUztfyMnGvvPyORYJNXfP7dcFM9HM\nldPF4vhoZ1c+ei0bJXfy0a2xYFe/TpzHdp2X7Oue9dHXfe1mvrnZd0+z0dIEW5JmzJih4uJibdu2\nreOehoZhaO3atUpKSgq7z+HpZs6cqeeee06rV6/WI488Ir//k6/233rrLe3atUv/8i//ooEDB/a4\nlrY2o9eXnjqhtbVNp05580U1GrW5/QbCif3NMXWWl/f3mchGe8TSMW9HzV334zVOH69YHB928lI2\nSu7mo1tjoa/9OnEe271v2Ndd92HXvnEz37ycrZYn2PPmzVNpaamWLFmiyspK5eTkqKysTLt371Zh\nYWHHJTvV1dWqrq5Wbm6ucnNzJX3yKeV3vvMdPfHEE/r2t7+tGTNmqL6+XiUlJUpNTdV9991n77MD\nAIeQjQAQjmwEEG8sT7CTkpJUUlKi4uJilZaWqqmpSTk5OVqxYoWmT5/e8bjy8nKtWbNGixYt6ghK\nSSosLNTo0aP15JNPasWKFUpOTtaXvvQl3X777brgAncuQwWAviIbASAc2Qgg3lieYEtSRkaGioqK\nVFRUFPExBQUFKigoMG3Ly8tTXl5eb7oGAM8iGwEgHNkIIJ549++bAwAAAAAQQ5hgAwAAAABgAybY\nAAAAAADYgAk2AAAAAAA2YIINAAAAAIANmGADAAAAAGCDXt2m68SJE1q1apV27typ+vp6jRw5UnPn\nztWsWbO6XXfTpk265557TNuuv/56/exnP+tNSQDgOrIRAMyRjwDiheUJdigU0oIFC3TgwAHNmTNH\nOTk52r59u5YuXar6+notXLiwy/Wrq6vl8/l0//33KyGhc/fnn3++1XIAwBPIRgAwRz4CiCeWJ9gl\nJSWqqqrSypUrNW3aNEnS7NmzlZ+fr9WrVysvL0+DBw+OuP5bb72lQYMG6frrr+991QDgMWQjAJgj\nHwHEE8u/wd6yZYuysrI6ArJdfn6+WlpatHXr1i7Xr66u1kUXXWS1WwDwNLIRAMyRjwDiiaUJdmNj\no2pqajRu3LiwtvZlFRUVEdc/evSojh8/3hGSH3/8sVpaWqyUAACeQzYCgDnyEUC8sTTBPnLkiAzD\n0JAhQ8La0tLSlJqaqoMHD0Zc/6233pIkHTx4UDNnztSll16q8ePH65vf/KZeeeUVi6UDgDeQjQBg\njnwEEG8sTbAbGhokSampqabtycnJam5ujrh+dXW1JOmNN97QddddpzVr1ujuu+9WbW2t8vPztWPH\nDivlAIAnkI0AYI58BBBvLP2RM8Mwum0PBAIR2y+99FL94Ac/0KxZszR8+HBJ0le+8hVdc801uu66\n61RUVKQpU6bI5/P1qB6/3ye/v2ePdVIg4O/0r5dEsza3n28g4FdCQnRq4Ji6I5rH1E7xmo0tLS2q\nrHzTlm35/T6lpZ2jxsaTamvren92Z+zYS5SYmGhLXV3xci5E4nTNXtw3TuVKLI6PaDgb89Fq9vUm\n3+zIMbvGoBNj2K7z0q3zLtb3tRNjWvLWuI4mSxPs9k8fQ6GQaXsoFNKIESMirj9x4kRNnDgxbPnQ\noUN11VVXqbS0VNXV1Ro9enSP6hkwILXHgeqG9PRkt0uIKBq1pacnS4ds36yl/jMyzD8ht7MPr+KY\nuides3HPnv264YliJWQPinpfPXWq9qh+e/u9pvszWrycC5E4VbMX943TueLFfeCkszEf9+zZr6/d\ntkRKObdP24mo+UO9+uSDtuVYX8egE2PY7vPSrfMuVvd11Me05LlxHU2WJtjDhw+Xz+dTXV1dWFtj\nY6Oam5tNf2PTEwMHDpQkNTU19XidY8eaPPsNdnp6soLBkFpb29wup5No1hYMmr94OiUYDOn48Z6P\nHys4pu6I5jG184U8XrMxGAwpIXuQEi8YFvW+rIjmuDmdl3MhEqdrdjtDzDA+ukc+di0YDH0yEemf\n2aftdNdHX8epXWPQifPYrvPSrfMu1ve1E2M6Ut9WuZmtPc1GSxPslJQUjRo1SpWVlWFte/fulSRN\nmDAh4vrf//739e677+o3v/mN+vXr16nt7bffliRdcMEFPa6nrc3o86WE0dTa2qZTp7z5ohqN2tx+\nA+HE/uaYOsvL+/t08ZqNbo+PSJweN7EyTk/nVM1eHCOMD2edjfnoxLi2c9z0dVux9nyjsT2n+nVr\nXzuV1V4a19Fk+eL1GTNmqLa2Vtu2betYZhiG1q5dq6SkpLB7HJ4uKytLf//73/Xss892Wr579269\n/PLL+tKXvqTMzOh+cgIA0UA2AoA58hFAPLH0DbYkzZs3T6WlpVqyZIkqKyuVk5OjsrIy7d69W4WF\nhR0hV11drerqauXm5io3N1eStHjxYr388su6//77VVVVpbFjx+rAgQP69a9/rSFDhmjZsmW2PjkA\ncArZCADmyEcA8cTyBDspKUklJSUqLi5WaWmpmpqalJOToxUrVmj69OkdjysvL9eaNWu0aNGijpAc\nNGiQNmzYoIceeki/+93vtGnTJmVmZmrWrFkqKCjgE0gAMYtsBABz5COAeGJ5gi1JGRkZKioqUlFR\nUcTHFBQUqKCgIGz5wIED9ZOf/KQ33QKAp5GNAGCOfAQQL7x7AzEAAAAAAGIIE2wAAAAAAGzABBsA\nAAAAABswwQYAAAAAwAZMsAEAAAAAsEGvJtgnTpzQ8uXLNXnyZI0fP155eXnasGFDrwpYuXKlRo8e\nrVdeeaVX6wOAV5CNABCObAQQTyzfpisUCmnBggU6cOCA5syZo5ycHG3fvl1Lly5VfX29Fi5c2ONt\nvfrqq3r88cfl8/mslgEAnkI2AkA4shFAvLE8wS4pKVFVVZVWrlypadOmSZJmz56t/Px8rV69Wnl5\neRo8eHC322loaNCSJUvUr18/tbS0WK8cADyEbASAcGQjgHhj+RLxLVu2KCsrqyMk2+Xn56ulpUVb\nt27t0XZ+/OMfyzAM3XTTTVZLAADPIRsBIBzZCCDeWJpgNzY2qqamRuPGjQtra19WUVHR7XY2b96s\n559/Xg888ID69+9vpQQA8ByyEQDCkY0A4pGlCfaRI0dkGIaGDBkS1paWlqbU1FQdPHiwy228//77\n+o//+A/NmzdPn/vc56xVCwAeRDYCQDiyEUA8sjTBbmhokCSlpqaaticnJ6u5uTni+m1tbbr77rs1\ndOhQ/fCHP7TSNQB4FtkIAOHIRgDxyNIfOTMMo9v2QCAQsf2Xv/yl9u3bp2effVaJiYlWujbl9/vk\n93vvL0kGAv5O/3pJNGtz+/kGAn4lJJjX0NLSosrKN3u9bb/fp7S0c9TYeFJtbV2fB2bGjr3EljFv\nJl6PqZfEaza6PT4icWrceDnrI3G6Zi/um+7GR19fL9r19XXjdNF8DYkmr2WjZE8+OjGu7cgxu873\nWHm+7ds5/V+nxPq+dvI1wSvjOposTbDbP4EMhUKm7aFQSCNGjDBt+8tf/qL//d//1YIFCzRo0CAd\nP35ckjo+uWxqatLx48d13nnn9fj2CwMGpHr6Vg3p6clulxBRNGpLT0+WDtm+WUv9Z2SYf0q+Z89+\nPfnyIxoQQs5QAAAgAElEQVR6YbbDVUmHa2p1W/odmjhxYlT7ibdj6iXxmo1ezTinx41X90NXnKrZ\ni/umu/GxZ89+3fBEsRKyBzlYVWSnao/qt7ffG/XXkGjwWjZK9uSjE+Pazhzra72x9nzbt+eGWN3X\nTr4meGVcR5OlCfbw4cPl8/lUV1cX1tbY2Kjm5mbT39lI0ssvv6zW1lY9+uijeuSRRzq1+Xw+FRQU\nyOfz6cUXX9TQoUN7VM+xY02e/QY7PT1ZwWBIra1tbpfTSTRrCwbNX0CdEgyGdPx4U8S2oRdmK+fi\nCxyu6p/9R6qtr+L1mPaVnS/k8ZqNbo+PSKI5bk7n5ayPxOmavThGuhsfwWBICdmDlHjBMAer6ppT\nY7qdXfnotWyU7MlHJ8a1HcfcrvM9Vp6v5F4ux/q+diqrvTSue6On2Whpgp2SkqJRo0apsrIyrG3v\n3r2SpAkTJpiu+41vfEOXXXZZ2PLNmzertLRUd999tz7zmc8oMzOzx/W0tRl9vuwqmlpb23TqlDff\ndEWjNrffYHb1nLxcm5f7iIf9Zod4zUa3x0ckTo+bWBmnp3OqZi+Oke6eeyzW7FVey0bJnnx0YozY\necz7uq1Ye77R2J5T/bq1r53KPS+N62iyNMGWpBkzZqi4uFjbtm3ruKehYRhau3atkpKSwu5z2G74\n8OEaPnx42PI///nPkqTPfOYz+vznP2+1HADwBLIRAMKRjQDijeUJ9rx581RaWqolS5aosrJSOTk5\nKisr0+7du1VYWNjxSWJ1dbWqq6uVm5ur3Nxc2wsHAC8hGwEgHNkIIN5YnmAnJSWppKRExcXFKi0t\nVVNTk3JycrRixQpNnz6943Hl5eVas2aNFi1aRFACOOuRjQAQjmwEEG8sT7AlKSMjQ0VFRSoqKor4\nmIKCAhUUFHS7rZ4+DgC8jmwEgHBkI4B44t0biAEAAAAAEEOYYAMAAAAAYAMm2AAAAAAA2IAJNgAA\nAAAANmCCDQAAAACADZhgAwAAAABgg17dpuvEiRNatWqVdu7cqfr6eo0cOVJz587VrFmzul23sbFR\n//M//6MdO3aorq5OQ4YMUV5enm699VYlJib2phwA8ASyEQDMkY8A4oXlCXYoFNKCBQt04MABzZkz\nRzk5Odq+fbuWLl2q+vp6LVy4MOK6H3/8sW699VZVVlbqhhtu0JgxY/T666/roYce0htvvKFHH320\nT08GANxCNgKAOfIRQDyxPMEuKSlRVVWVVq5cqWnTpkmSZs+erfz8fK1evVp5eXkaPHiw6bqbNm3S\n3r17VVhYqO985zsd66alpWndunXatWuXvvjFL/bh6QCAO8hGADBHPgKIJ5Z/g71lyxZlZWV1BGS7\n/Px8tbS0aOvWrRHXbWpq0ujRo/XNb36z0/IvfvGLMgxD+/fvt1oOAHgC2QgA5shHAPHE0gS7sbFR\nNTU1GjduXFhb+7KKioqI63/nO9/R5s2blZaW1ml5ZWWlfD6fhg0bZqUcAPAEshEAzJGPAOKNpUvE\njxw5IsMwNGTIkLC2tLQ0paam6uDBgz3aVktLiw4ePKjy8nL97//+ry655BJdffXVVsoBAE8gGwHA\nHPkIIN5YmmA3NDRIklJTU03bk5OT1dzc3KNtPfXUU3rggQfk8/k0YMAALVu2TP369bNSDgB4AtkI\nAObIRwDxxtIE2zCMbtsDgUCPtjVhwgT98pe/1OHDh/X4449r9uzZeuihhzR58uQe1+P3++T3+3r8\n+J5qaWlRZeWbvV7f7/cpLe0cNTaeVFtb1/vMzNixl0TtthOBgL/Tv9HYtlsCAb8SEsxr8HJtdmz7\n9H+jsW23RHO/2SlesvFMbo+PSJwaN9E896LF6Zq9uG+6Gx+xWLOXnY356MQYseOY23W+u/l8rb4n\n7817cDved8f6vnbyNcEr4zqaLE2w2z99DIVCpu2hUEgjRozo0bZO/y3OlClTNH36dC1fvtxSSA4Y\nkCqfz/43kXv27NeTLz+ioRdm277t7hyuqdVt6Xdo4sSJUe0nPT05Ots8ZPtmLfWfkWH+CbmXa7Oz\nj6hs8yzfb3aIl2w8UzTGnB2cHjde3Q9dcapmL+6b7sZHLNbsZWdjPjoxRuw85n2t183nu2fPfn3t\ntiVSyrnR6bj5Q7365IO2ve+O1X3t5GuCV8Z1NFmaYA8fPlw+n091dXVhbY2NjWpubjb9jU13srOz\nNXHiRP3ud7/TsWPHNGDAgB6td+xYU1S+pQkGQxp6YbZyLr7A9m33tP/jx5uisu1AwK/09GQFgyG1\ntrbZuu1g0PzF0yld7Tcv19ZX8XpM+8rON6vxko1ncnt8RBLNcXO6aJ570eJ0zV4cI92Nj1is2W7k\nY9ecGCN2HHO7znc3n28wGPpkct0/0/G+rYj1fe1U7nlpX/dGT7PR0gQ7JSVFo0aNUmVlZVjb3r17\nJX1y+U4k+fn5ev/99/XCCy+EfXrY1NQkn89n6RKNtjajV5dgd8ftN0qtrW06dSq6NUSjDy/vNy/X\n5uU+4mG/2SFesvFMbo+PSJweN7EyTk/nVM1eHCPdPfdYrNnLzsZ8dGKM2HnM+7otN58v+9p+ZjU6\nlXte2tfRZPni9RkzZqi2tlbbtm3rWGYYhtauXaukpKSwexyebtiwYXr//fe1adOmTstfe+01vfba\na/r85z8fdhsGAIgFZCMAmCMfAcQTS99gS9K8efNUWlqqJUuWqLKyUjk5OSorK9Pu3btVWFiozMxP\nLuGorq5WdXW1cnNzlZubK0m6/fbbtWvXLi1btkyVlZUaPXq0/vrXv+qZZ57RwIEDtWzZMlufHAA4\nhWwEAHPkI4B4YnmCnZSUpJKSEhUXF6u0tFRNTU3KycnRihUrNH369I7HlZeXa82aNVq0aFFHSGZm\nZuq5557TQw89pB07duiZZ55RZmamZs6cqUWLFikrK8u+ZwYADiIbAcAc+QggnlieYEtSRkaGioqK\nVFRUFPExBQUFKigoCFveft9CPnEEcLYhGwHAHPkIIF549wZiAAAAAADEECbYAAAAAADYgAk2AAAA\nAAA2YIINAAAAAIANmGADAAAAAGCDXv0V8RMnTmjVqlXauXOn6uvrNXLkSM2dO1ezZs2ytO7Ro0fV\nv39/TZo0SbfffrtGjRrVm3IAwBPIRgAwRz4CiBeWJ9ihUEgLFizQgQMHNGfOHOXk5Gj79u1aunSp\n6uvrtXDhwojrtrS06JZbbtG7776rmTNnauzYsTp48KDWrVunl19+WevXr9enP/3pPj0hAHAD2QgA\n5shHAPHE8gS7pKREVVVVWrlypaZNmyZJmj17tvLz87V69Wrl5eVp8ODBpuuuXbtWBw4c0P3336+Z\nM2d2LJ86dapmz56tFStW6LHHHuvlUwEA95CNAGCOfAQQTyz/BnvLli3KysrqCMh2+fn5amlp0dat\nWyOu+//+3/9TUlKSrr/++k7Lx4wZo0996lN67bXXrJYDAJ5ANgKAOfIRQDyx9A12Y2OjampqNGXK\nlLC2cePGSZIqKioirl9cXKz6+nr5fL6wtkjLAcDryEYAMEc+Aog3libYR44ckWEYGjJkSFhbWlqa\nUlNTdfDgwYjrZ2ZmKjMzM2z55s2b9cEHH+irX/2qlXIAwBPIRgAwRz4CiDeWLhFvaGiQJKWmppq2\nJycnq7m52VIBb731lpYvX66EhAQtXrzY0roA4AVkIwCYIx8BxBtL32AbhtFteyAQ6PH23nzzTX33\nu99Vc3OzfvzjH2vMmDFWypHf75Pfb/+lQYGAu7cHDwT8SkiITg3tzy0az9HL+83LtbW0tKiy8s1e\nb9vv9ykt7Rw1Np5UW1vX56iZsWMvUWJiommbl/ebl8RLNp7J7fERSXfjpq/nXLu+nnun6+o8tFM0\nXwO66s9LuhsfsVizl52N+ejEGDE75lazqzcZZZZFbj1ft/u2uo3T/+3rdqLJ7Pk6+ZrglX0dTZYm\n2O2fPoZCIdP2UCikESNG9GhbL730ku6880599NFHWrp0qW666SYrpUiSBgxIjcpvb9LTk6VDtm/W\nUv8ZGeaf9NrZR1S26dH95uXa9uzZrydffkRDL8x2uCrpcE2tbku/QxMnTjRt9/J+85J4ycYzRSNH\n7NDduNmzZ79ueKJYCdmDHKwqslO1R/Xb2++NeB5Gg1PHzotjpLvxEYs1e9nZmI9OjBGzY75nz359\n7bYlUsq50em0+UO9+uSDYVnk1vN1u+/ebsvN9Xvax5nP18nXBK/s62iyNMEePny4fD6f6urqwtoa\nGxvV3Nxs+hubMz311FP66U9/qkAgoF/84hf6+te/bqWMDseONUXlW5pg0PxFwCnBYEjHjzdFZduB\ngF/p6ckKBkNqbW2zddte3m9er23ohdnKufgCh6v6Z/+xuN/6ys43q/GSjWdye3xE0t24CQZDSsge\npMQLhjlYVdeiOdZPF83XADNeHCM9GR9e49T4aEc+ds2JMWJ2zIPB0CeT6/7hv0mPer9RFmmMu9m3\nFXZlq6tjywFe2te90dNstDTBTklJ0ahRo1RZWRnWtnfvXknShAkTutzGE088oQceeEDnnnuu1qxZ\no8svv9xKCZ20tRl9vizPjNMHy6z/U6eiW0M0+vDyfqO2yGK1Ni+Jl2w8k9vjI5Luxo0X63Z6rDvV\nXyzu61is2cvOxnx0YoyYHfN469ftvt3Y1tl8jCP17YVt2c3yxeszZsxQbW2ttm3b1rHMMAytXbtW\nSUlJYfc4PN0f/vAH/fznP1dGRobWrVvXp4AEAC8hGwHAHPkIIJ5Y+gZbkubNm6fS0lItWbJElZWV\nysnJUVlZmXbv3q3CwsKOWylUV1erurpaubm5ys3NlWEY+ulPfypJ+upXv6r9+/dr//79YdufMWNG\nH58SADiPbAQAc+QjgHhieYKdlJSkkpISFRcXq7S0VE1NTcrJydGKFSs0ffr0jseVl5drzZo1WrRo\nkXJzc1VTU6O///3vkqRNmzZp06ZNptu/7rrr5Pd796/CAYAZshEAzJGPAOKJ5Qm2JGVkZKioqEhF\nRUURH1NQUKCCgoKO/48aNUpVVVW96Q4AYgLZCADmyEcA8YKP+wAAAAAAsAETbAAAAAAAbMAEGwAA\nAAAAG/TqN9gAAAAAcDZqaWnRvn1v9vjxgYBf6enJCgZDPb6n9MUXX6LExMTelggPY4INAAAAAP+/\nffve1DWL75VSzo1OB80f6oVV9+uzn70sOtuHq5hgAwAAAMDpUs6V+me6XQViUK9+g33ixAktX75c\nkydP1vjx45WXl6cNGzZY3k4wGNSVV16pBx98sDdlAICnkI0AEI5sBBBPLH+DHQqFtGDBAh04cEBz\n5sxRTk6Otm/frqVLl6q+vl4LFy7s0XZOnjyp2267TUePHrVcNAB4DdkIAOHIRgDxxvIEu6SkRFVV\nVVq5cqWmTZsmSZo9e7by8/O1evVq5eXlafDgwV1u469//avuvPNOvf32272rGgA8hmwEgHBkI4B4\nY/kS8S1btigrK6sjJNvl5+erpaVFW7du7XL9hx9+WNdff72OHj2q+fPnyzAMqyUAgOeQjQAQjmwE\nEG8sTbAbGxtVU1OjcePGhbW1L6uoqOhyG1VVVZo1a5a2bdumr371q1a6BwBPIhsBIBzZCCAeWbpE\n/MiRIzIMQ0OGDAlrS0tLU2pqqg4ePNjlNn7xi1+oX79+kqR33nnHSvcA4ElkIwCEIxsBxCNL32A3\nNDRIklJTU03bk5OT1dzc3OU22kMSAM4WZCMAhCMbAcQjS99gd/e7F8MwFAgE+lSQFX6/T36/z/bt\nBgK9unuZrf0nJJjX0NLSosrKN3u9bb/fp7S0c9TYeFJtbdZ/xzR27CVKTEw0bfPyfqO2yGK1Ni+J\nl2w8k9vjI5Luxo0X6+6u5r5mf7u+vgacqavXBCk293Us1uxVXstGyZ58dGKMmB3zeOvXzb7p17m+\nrb6+9eZ1rLvXKrtZmmC3fwIZCoVM20OhkEaMGNH3qnpowIBU+Xz2v4lMT0+WDtm+WUv9Z2SYf9q7\nZ89+PfnyIxp6YbbDVUmHa2p1W/odmjhxomm7l/cbtUUWq7V5Sbxk45nS05Oj3kdvdDduvFh3dzXv\n2bNfNzxRrITsQQ5W1bVTtUf129vvjfiaIMXmvo7Fmr3Ka9ko2ZOPTowRs2Meb/262Tf9Otf3nj37\n9bXblkgp50an0+YP9eqTD3b5WmU3SxPs4cOHy+fzqa6uLqytsbFRzc3Npr+ziZZjx5qi8i1NMGj+\nQuCUYDCk48ebIrYNvTBbORdf4HBV/+y/q9rcRG29E6u19ZWdb1bjJRvP5Pb4iKS7cePFuntSc0L2\nICVeMMzBqrp3tu5rr4lmFpqxKx+9lo2SPfnoxBgxO+bx1q+bfdOvw32nnCv1z3S0397oaTZammCn\npKRo1KhRqqysDGvbu3evJGnChAlWNtknbW2GLZe4nam1tc32bVrt/9Qp8xqoLTJq651Yrc1L4iUb\nz+T2+Iiku3HjxbpjsWYpNus+G2v2Kq9lo2RPPjoxRsyOebz162bf9Ht29e10hlq+4H7GjBmqra3V\ntm3bOpYZhqG1a9cqKSkp7D6HABAPyEYACEc2Aog3lr7BlqR58+aptLRUS5YsUWVlpXJyclRWVqbd\nu3ersLBQmZmffL1fXV2t6upq5ebmKjc31/bCAcBLyEYACEc2Aog3lifYSUlJKikpUXFxsUpLS9XU\n1KScnBytWLFC06dP73hceXm51qxZo0WLFnUZlD6fz5E/xgMA0UQ2AkA4shFAvLE8wZakjIwMFRUV\nqaioKOJjCgoKVFBQ0OV2Jk2apKqqqt6UAACeQzYCQDiyEUA8ib2bKgIAAAAA4EFMsAEAAAAAsAET\nbAAAAAAAbMAEGwAAAAAAGzDBBgAAAADABr2aYJ84cULLly/X5MmTNX78eOXl5WnDhg09WretrU1P\nPPGEpk2bpvHjx2vy5MkqLi7WRx991JtSAMAzyEYAMEc+AogXlm/TFQqFtGDBAh04cEBz5sxRTk6O\ntm/frqVLl6q+vl4LFy7scv1ly5bpmWee0dSpUzVv3jzt27dPjzzyiPbv369HH320108EANxENgKA\nOfIRQDyxPMEuKSlRVVWVVq5cqWnTpkmSZs+erfz8fK1evVp5eXkaPHiw6boVFRV65plndOONN+on\nP/lJx/Ls7Gw99NBDev755zV16tRePhUAcA/ZCADmyEcA8cTyJeJbtmxRVlZWR0C2y8/PV0tLi7Zu\n3Rpx3Y0bN8rn82n+/Pmdls+fP18JCQnauHGj1XIAwBPIRgAwRz4CiCeWJtiNjY2qqanRuHHjwtra\nl1VUVERcv6KiQv3791dOTk6n5cnJybrooov0l7/8xUo5AOAJZCMAmCMfAcQbSxPsI0eOyDAMDRky\nJKwtLS1NqampOnjwYMT16+rqTNeVpMGDBysYDKqxsdFKSQDgOrIRAMyRjwDijaUJdkNDgyQpNTXV\ntD05OVnNzc1drp+SkhJxXemTP4QBALGEbAQAc+QjgHhj6Y+cGYbRbXsgEOjV+u1tXa1/Jr/fJ7/f\n1+PH91Qg4Nfhmlrbt9sTh2tqFRjmV0KC+Wcf1GaO2nonlmvzknjJxjMFAn6dqj0a9X6sOFV7VIFA\n1+PGa3XHYs1SbNZ9ttbsZWdjPgYCfqn5wz5to0vNH5oe83jr182+6fcs6ruL8RUtlibY7Z8+Rvqk\nMBQKacSIEV2uf/LkyYjrSp9cLtRTAwf2/LFWTJnyZU2Z8uWobLuvqK13qK13vFybl8RLNp5pypQv\n63gMjo9YrDsWa5Zis+5YrNnLzsZ8nDLlyzKq/9jn7dCvd/um3/joO1osTeWHDx8un8+nurq6sLbG\nxkY1NzdH/J1M+/pm60qf/EYnIyNDiYmJVkoCANeRjQBgjnwEEG8sTbBTUlI0atQoVVZWhrXt3btX\nkjRhwoSI648fP14ffvih3n///U7Lm5ubdeDAgS7XBQCvIhsBwBz5CCDeWL4YfcaMGaqtrdW2bds6\nlhmGobVr1yopKSnsHoenmz59ugzD0OOPP95p+a9+9Su1trbq+uuvt1oOAHgC2QgA5shHAPEksGzZ\nsmVWVhg7dqzKy8u1YcMGNTQ06PDhw/rFL36hP/3pT/rRj36kL3zhC5Kk6upq/fGPn1xPn5mZKUnK\nzs7WoUOHtGHDBr399ttqbGzU008/rSeeeEKTJ09WQUGBvc8OABxCNgKAOfIRQDyxPMFOSEjQtdde\nqxMnTuj555/XSy+9pJSUFN1999268cYbOx63fv163X///Ro4cKAmTZrUsXzy5MlKTEzUH/7wB5WV\nlenDDz/ULbfcoqVLl1r6K5AA4CVkIwCYIx8BxBOf0d39EwAAAAAAQLdi86aKAAAAAAB4DBNsAAAA\nAABswAQbAAAAAAAbMMEGAAAAAMAGCW4XcDa66qqr9P777+t73/uefvjDH7payz333KNNmzZ1Wubz\n+dS/f3+NGjVKs2fPdv0ekjt37tSmTZtUWVmpDz74QKmpqRo7dqy+9a1vacqUKY7Xs3r1aq1evbrT\nMr/fr3POOUfDhg3TV77yFeXn5+u8885zvLZI9ZmZN2+e7rnnHgcq+qdNmzZ126fP59OePXuUlpbm\nUFWIBV7KzUhiIU8j8VrOdsXrGRyJl7MZ7nIq39zOKKdzxs2scPN8d/O91uuvv66NGzfq9ddf15Ej\nR9TW1qbs7Gx94Qtf0Ny5c3X++efb2t+qVau0Zs0aPfDAA/rGN75h+pj2/VFQUOCZ2/YxwbbZq6++\nqvfff1+pqanasGGDFi9erIQEd3ezz+fT97//fV144YWSpFOnTunEiRN66aWXdM899+jw4cNatGiR\n43U1NTXpnnvu0W9/+1uNGTNGN9xwgwYNGqS6ujpt2bJFixYtcu2NiM/n0+zZs3X55ZdLklpbW9XQ\n0KC9e/fq8ccf16ZNm/TUU0/ZHiS9rc/MqFGjHKyos6uvvlpXXXVVxPbk5GQHq4HXeTE3I/Fqnkbi\n5ZztitczOBKvZzOc53S+uZFRbuaMm1nh9vnu5Hutjz/+WA888IDWrVunoUOHaurUqRo5cqQMw9C+\nffu0ceNGrV+/Xv/5n/+pqVOn2tavz+eTz+fr0eM8xYCt7rrrLuPiiy82Vq1aZeTm5hplZWWu1rNk\nyRJj9OjRxquvvhrW1traauTl5Rnjxo0zgsGg47XdcccdxujRo41HH300rK2lpcWYP3++kZuba6xb\nt87RulatWmWMHj3a2LRpk2n7rl27jDFjxhhTp041WltbHa3NMLqvz00bN240cnNzjVWrVrldCmKI\n13IzEi/naSRezdmueD2DI/FyNsM9TuabWxnlVs64mRVunu9uvNd64IEHjNzcXOO+++4zWlpawtoP\nHz5sTJkyxbj00kuNw4cP29ZvT/azF9978htsGzU1Nam8vFyXXHJJxyU469evd7mqyPx+vz7/+c+r\npaVF7733nqN979q1S88//7yuvvpq3XrrrWHt/fr10/3336+EhAStW7fO0dq6c8UVV2j+/Pl67733\nVFpa6nY5QEyLtdyMxM08jSSWc7YrZDBihZfyLVoZ5eWcISvs8dZbb+mJJ57QmDFj9JOf/ET9+vUL\ne0x2drbuu+8+nTx5Us8884wLVXoLE2wb/eY3v1EoFNIVV1yhYcOGady4cdqzZ49qamrcLi2igwcP\nKhAIaPjw4Y72u3nzZvl8Pt1yyy0RH5Odna3S0lJPhuINN9wgwzD04osvul0KENNiMTcjcStPI4n1\nnO0KGYxY4LV8i0ZGeT1nyIq+27hxoyRp8eLF8vsjTx2vvPJKPfbYY/rBD37gVGme5c0fucWoDRs2\nyOfz6dprr5UkTZs2TRUVFVq/fr3uvfdeV2traGjQ8ePHJUmGYejEiRPavn27duzYoYULFyojI8PR\net58800FAgGNHz++y8e1/4bIa3JycnTOOedo3759rtXQ1NTUcUzNOH1MT3fy5MmItblZF7zHy7kZ\nidfyNJJYz9mueCGDI/FyNsNZbuWbkxnl9ZyJdla4eb479V7rlVdekc/n0+c///kuH+fz+XTFFVfY\n1u/putrPTU1NUemzL5hg2+Sdd95RRUWFRo8e3fEHDaZNm6YVK1Zoy5Yt+tGPfqTExERXajMMQ7fd\ndptp2+WXX67vfe97DlckHT16VOedd57pZSax4txzz9WxY8dc6dswDC1fvlzLly83bXf7L3U//vjj\neuyxx8KW+3w+VVVVuVARvMjLuRmJF/M0krMhZ7viZgZH4vVshnPcyjenMyoWciZaWeH2+e7Ue63a\n2lplZGTonHPOCWszm/QGAgGlp6fb1n93+1ny3h85Y4Jtk+eee04+n09f//rXO5YNGjRIl19+ufbs\n2aOysjLXbt/i8/lUWFio3NxcSZ8M1GAwqNdee03r16/XzJkz9dRTT2nAgAGO1RQIBNTW1uZYf9Hw\n8ccfu3ZC+3w+5efnd/lJYUpKioMVdZaXl6e8vDzX+kds8HJuRuLFPI3kbMjZrriZwZF4PZvhHLfy\nzemMioWciVZWuH2+O/Veq62tLeIxNvtWe8iQIfrd735nW//d7eddu3bp8ccft60/OzDBtkFra6u2\nbt0qSRo/frwOHTrU0fa5z31Or776qp5++mlX3yhefPHFmjhxYqdlU6dOVU5OjpYvX65f/vKXuu++\n+xyrZ/DgwXrvvff08ccfe/pTz0haW1sVDAY1ePBg12r41Kc+1e3lOm4ZPny4Z2uDN8RCbkbitTyN\nJNZztiteyOBIvJzNcIbb+eZkRnk9Z6KdFW6e706918rOzta7775reox/9atfdfr/XXfdFZUautrP\ndXV1UemzL5hg22Dnzp36xz/+IZ/Pp7lz53Zqa//E7M0331RVVZU+85nPuFFiRHl5eVq+fLn+/Oc/\nO9rvxIkTVVNTozfeeEOTJk2K+Lh///d/V1NTk+666y4NGTLEwQq7VlVVpVOnTmns2LFulwLEpFjO\nzSCCcA8AACAASURBVEjcytNIYj1nu0IGw8u8mm/RyCiv5wxZ0Xftx/iPf/yjrrzyyk5tZ056ExMT\nPX9FgxOYYNug/TKg7373u6Z/5GHTpk168cUX9fTTT6uoqMiFCiNrPwmcvszuuuuu0/r16/Xkk09G\nDOSjR49q06ZNSklJ0c9+9jNH6+vOli1b5PP5NHXqVLdLAWJSLOdmJG7laSSxnrNdIYPhZV7Nt2hk\nlNdzhqzou29+85v69a9/rUcffVRf/vKXPfMa52VMsPuovr5eu3btUnp6uhYtWqSkpKSwx4wYMUI7\nduzQb37zGxUWFio1NdWFSs21/+n9L33pS472e/nll+uqq65SeXm5HnvssbB7JzY2Nur222/XqVOn\ntGjRIk/9oaP2S7s+9alP6ZprrnG7HCDmxHpuRuJWnkYSyznbFTIYXublfItGRnk5Z8gKe1x88cXK\nz8/X448/rsLCQv3kJz9RcnJyp8e0tLToV7/6lY4cOaJBgwa5VKl3MMHuo40bN+rUqVOaOXOmaYhK\n0qc//Wl94Qtf0CuvvKItW7bo29/+tqM1GoahXbt2qba2tmPZRx99pD/96U96/vnnNWzYMC1YsMDR\nmiTp/vvv14cffqiVK1dq27ZtuuaaazRgwAC9++672rJli44dO6abbrop7PIqJxiGoddff73jfn9t\nbW0KBoPau3evfvvb3yozM1OrV6/u8n6ATtZnpl+/fh23BgG8JBZyMxKv5mkkXs7Zrng9gyMhm+F2\nvrmRUW7mjJtZEU/n+5133qlAIKDHHntMu3bt0jXXXKOLLrpIfr9fBw4c0AsvvKD6+noNGzZMS5cu\ntbVvwzBs3Z4TmGD30ebNmxUIBHTTTTd1+bj58+frlVde0a9//WvH3yj6fD498sgjnZadc845GjZs\nmObOnatbb71V5557rqM1SVL//v21du1alZWVafPmzVq/fr3+8Y9/KC0tTePHj9fNN9/s2jdBPp9P\nzz77rJ599tmO/6ekpOiCCy7Q9773Pc2dO9eVfRapPjP9+/d3JdR9Ph+XD6FLsZCbkXg1TyPxcs52\nxesZHImXsxnOcDvf3MgoN3PGzaxw83x3+r2Wz+fTD3/4Q1133XXauHGj/vjHP2rbtm366KOPNHDg\nQE2aNEnXXHONrrrqKts/zOjJ8/Tae0+fEYsfCwAAAAAA4DHeurYKAAAAAIAYxQQbAAAAAAAbMMEG\nAAAAAMAGTLABAAAAALABE2wAAAAAAGzABBsAAAAAABswwQYAAAAAwAZMsAEAAAAAsAETbAAAAAAA\nbMAEGwAAAAAAGzDBBgAAAADABkywAQAAAACwARNsAAAAAABswAQbAAAAAAAbMMEGAAAAAMAGTLAB\nAAAAALABE2wAAAAAAGzABBsAAAAAABswwQYAAAAAwAZMsAEAAAAAsAETbAAAAAAAbMAEGwAAAAAA\nGzDBBgAAAADABn2aYP/lL3/RmDFj9Morr/R4nU2bNun666/XZz/7WX3xi19UUVGRgsFgX8oAAE8h\nGwHAHPkI4GzX6wn2e++9p0WLFskwjB6v8/DDD+uee+7RgAEDdNddd2nGjBl69tlnNW/ePLW0tPS2\nFADwDLIRAMyRjwDiQUJvViovL9d9991n6dPDI0eOaPXq1bryyiv18MMPdywfPXq07r77bpWUlCg/\nP7835QCAJ5CNAGCOfAQQLyx/g71w4UItXrxYgwYN0te//vUer1daWqpTp05p7ty5nZbPmDFDgwcP\n1saNG62WAgCeQTYCgDnyEUA8sTzBfu+993TnnXdq48aNGjlyZI/Xq6iokCSNHz8+rG3cuHGqqalR\nY2Oj1XIAwBPIRgAwRz4CiCeWLxEvKytTv379LHdUV1enlJQUpaWlhbUNHjxYknTo0CHl5uZa3jYA\nuI1sBABz5COAeGL5G+zeBKQkNTQ0KCUlxbQtOTlZkhQKhXq1bQBwG9kIAObIRwDxxLH7YHf1FyPb\n2/x+bssNIL6QjQBgjnwEEIscS6XU1FSdPHnStK19ef/+/S1t08ptHgDAi8hGADBHPgKIRb26TVdv\nDB8+XFVVVWpubg673Keurk5+v7/j9zQ9dexYk/x+n51l2iIQ8Cs9PVnBYEitrW1ul9MJtfUOtVnn\n1braZWSkul2CpPjKxq54fbyYoWbnxGLdsVhzO/LRXm6NhXjr182+6dc5bvbd02x0bII9fvx4lZeX\nq6KiQv/yL//Sqa2iokIXXXRRxN/ZRNLWZqitzbufRLa2tunUKW++qFJb71CbdV6tyyviMRu7Eovj\nhZqdE4t1x2LNXnG25aNbYyHe+nWzb/qNj76749gl4tdee60CgYDWrl3bafnmzZt19OhRzZw506lS\nAMAzyEYAMEc+AohFUfkG+/3339cbb7yh888/X5deeqkkaejQofr+97+vNWvWaMGCBbr22mtVU1Oj\nJ598UuPHj9dNN90UjVIAwDPIRgAwRz4COFtEZYL92muv6d5779U3vvGNjpCUpIKCAmVlZenJJ5/U\n8uXLlZmZqZtuukm33367EhMTo1EKAHgG2QgA5shHAGcLnxHDf07xgw8a3C7BVEKCXxkZqTp+vMlz\nvw2gtt6hNuu8Wle7rCxrf3k2lng1G7vi9fFihpqdE4t1x2LN7chHe7k1FuKtXzf7pl/nuNl3T7OR\nmwcCAAAAAGADJtgAAAAAANiACTYAAAAAADb4/9q7++goCnv/45/ZDQlJIBogQCS0RqxBQGKB4hV7\nrZIfElMlLfUGWnk6RPFWsF6vykPx3KJcuVTL5VjA04M8eE6qxgcIgfLQgthWioqViyERUjR6K/JY\nIOQRQ5L5/eFJLnF3k0wy2Zlh369/OMzs7Pe7m8kn+92dnWHABgAAAADABgzYAAAAAADYgAEbAAAA\nAAAbMGADAAAAAGADBmwAAAAAAGzAgA0AAAAAgA0YsAEAAAAAsAEDNgAAAAAANmDABgAAAADABgzY\nAAAAAADYgAEbAAAAAAAbMGADAAAAAGADBmwAAAAAAGzAgA0AAAAAgA0YsAEAAAAAsAEDNgAAAAAA\nNmDABgAAAADABgzYAAAAAADYgAEbAAAAAAAbRHVko/Lycq1YsUJvvfWWzpw5o6uvvlrTpk3Tj370\noza3ra6u1nPPPaddu3bp1KlT6t27t8aNG6d/+7d/U48ePTrSDgC4AtkIAIHIRgCRxPKAXVtbq5kz\nZ+rIkSOaMmWKUlNTtX37di1cuFBnzpzRrFmzQm7b0NCgGTNmqLi4WFlZWRo9erRKSkr08ssva//+\n/crPz1d0dHSnHhAAOIFsBIBAZCOASGN5wM7Ly9OhQ4e0bNkyZWVlSZJycnKUm5urlStXKjs7W/36\n9Qu67a5du3Tw4EHl5OToqaeeal7et29frVq1Sps2bVJOTk4HHwoAOIdsBIBAZCOASGP5O9iFhYVK\nSkpqDskmubm5qqur05YtW0Ju+7//+78yDEO33XZbi+UZGRkyTVMfffSR1XYAwBXIRgAIRDYCiDSW\nBuyqqiqVlZVp+PDhAeualhUVFYXc/pprrpFpmvr4449bLP/0008lScnJyVbaAQBXIBsBIBDZCCAS\nWTpE/OTJkzJNU/379w9Y16NHD8XHx+vo0aMht8/IyNAdd9yh1atXq2/fvho9erQOHz6spUuXKjk5\nWffcc4/1RwAADiMbASAQ2QggElkasCsrKyVJ8fHxQdfHxsaqpqYm5PaGYejBBx/UJ598ovnz5zcv\nT0pK0tq1a9W7d28r7QCAK5CNABCIbAQQiSwN2KZptrne7/eHXP/ee+/p/vvvV7du3fTQQw/p+uuv\n19GjR7V+/XpNnjxZv/nNbzRixIh29+PzGfL5jHbfPlz8fl+Lf92E3jqG3qxza19dgWzsPC/uL/Qc\nPl7s24s9281t2Sg5k49O7QuRVtfJ2tSNjNrtZWnAbnoHsra2Nuj62tpaDRw4MOT2y5cvV319vdav\nX6+RI0c2L8/KytKECRP02GOPaefOna2G7aV69YqXYbj3RWRCQqzTLYREbx1Db9a5tS87kY328eL+\nQs/h48W+vdizXdyWjZKz+ejUvhBpdZ2sTd3IqN0WSwN2SkqKDMPQiRMnAtZVVVWppqYm6PdsmpSW\nlurqq69uEZKS1KdPH2VkZOiNN97QJ598ouuuu65d/Zw9W+3KT2n8fp8SEmJVUVGrhoZGp9tpgd46\nht6sc2tfTRITgx+y2BFkY+e5fX8Jhp7Dx4t9e7HnJnblo9uyUXImH53aFyKtrpO1qRs+TtZubzZa\nGrDj4uI0aNAgFRcXB6w7cOCAJLV6qE5MTIwaGhqCrmta3tjY/ieqsdFUY2Prhx85qaGhUfX17vyj\nSm8dQ2/WubUvO5GN9vHi/kLP4ePFvr3Ys13clo1f3d65fHRqX4i0uk7Wpm5k1G6L5YPXJ0yYoOPH\nj2vbtm3Ny0zT1Lp16xQTExNwncNL3Xbbbfr73/+u3bt3t1h+7Ngx7dq1S/369VNaWprVlgDAcWQj\nAAQiGwFEGkufYEvS9OnTtXnzZs2fP1/FxcVKTU3V1q1b9d5772nevHnq06ePpK8O6yktLVVaWlpz\n+D366KPat2+fHn74YU2cOFHDhg3TF198ofz8fNXW1uq///u/Pfu9QQCRjWwEgEBkI4BI41+0aNEi\nKxtERUXpzjvvVHl5uXbs2KHdu3crLi5Oc+fO1aRJk5pvl5+fryVLlqh3794aPXq0pK9OdjFhwgTV\n1NToT3/6k7Zt26a//e1vGj16tH75y18GfMemLTU1dZZuHy4+n6HY2GhduHDRdYdp0lvH0Jt1bu2r\nSXx8jK33RzZ2jtv3l2DoOXy82LcXe25iZz66KRslZ/LRqX0h0uo6WZu64eNk7fZmo2G2dQ0FFzt9\nutLpFoKKivIpMTFe585Vu+67AfTWMfRmnVv7apKU1NPpFrqMW7OxNW7fX4Kh5/DxYt9e7LkJ+Wgv\np/aFSKvrZG3qho+Ttdubje69gBgAAAAAAB7CgA0AAAAAgA0YsAEAAAAAsAEDNgAAAAAANmDABgAA\nAADABgzYAAAAAADYgAEbAAAAAAAbMGADAAAAAGADBmwAAAAAAGzAgA0AAAAAgA0YsAEAAAAAsAED\nNgAAAAAANmDABgAAAADABgzYAAAAAADYgAEbAAAAAAAbMGADAAAAAGADBmwAAAAAAGzAgA0AAAAA\ngA0YsAEAAAAAsAEDNgAAAAAANmDABgAAAADABgzYAAAAAADYoEMDdnl5uRYvXqyxY8cqPT1d2dnZ\n2rBhQ7u3f/vttzV16lSNHDlSN910k3Jzc3Xw4MGOtAIArkE2AkAgshFAJLE8YNfW1mrmzJl67bXX\nNH78eC1cuFC9evXSwoULtXr16ja3f/311zVr1ixVVlbq3//935Wbm6vS0lJNmTJFJSUlHXoQAOA0\nshEAApGNACJNlNUN8vLydOjQIS1btkxZWVmSpJycHOXm5mrlypXKzs5Wv379gm578uRJLVmyRDfc\ncIPy8vIUExMjScrMzFRWVpaee+65doUtALgN2QgAgchGAJHG8ifYhYWFSkpKag7JJrm5uaqrq9OW\nLVtCbltQUKALFy5o7ty5zSEpSd/4xje0YMECjRkzxmo7AOAKZCMABCIbAUQaS59gV1VVqaysTBkZ\nGQHrhg8fLkkqKioKuf2+ffsUHx+vkSNHSpIaGhp08eJFde/eXffee6+VVgDANchGAAhENgKIRJY+\nwT558qRM01T//v0D1vXo0UPx8fE6evRoyO0/+eQTJScn629/+5tmzpyp4cOH68Ybb9Tdd9+tP/3p\nT9a7BwAXIBsBIBDZCCASWRqwKysrJUnx8fFB18fGxqqmpibk9hUVFTp//rzuvfdeJSUlafny5Vq0\naJFqamr005/+VG+++aaVdgDAFchGAAhENgKIRJYOETdNs831fr8/5Pq6ujqdPn1aM2bM0Lx585qX\nZ2RkKDMzU08//XTQw4hC8fkM+XxGu28fLn6/r8W/bkJvHUNv1rm1r65ANnaeF/cXeg4fL/btxZ7t\n5rZslJzJR6f2hUir62Rt6kZG7fayNGA3vQNZW1sbdH1tba0GDhwYcvvY2FhVV1frJz/5SYvlSUlJ\nuv3227V161aVlZXpmmuuaVc/vXrFyzDc+yIyISHW6RZCoreOoTfr3NqXnchG+3hxf6Hn8PFi317s\n2S5uy0bJ2Xx0al+ItLpO1qZuZNRui6UBOyUlRYZh6MSJEwHrqqqqVFNTE/R7Nk2Sk5P18ccfq0+f\nPgHrmpZVVVW1u5+zZ6td+SmN3+9TQkKsKipq1dDQ6HQ7LdBbx9CbdW7tq0liYvBDFjuCbOw8t+8v\nwdBz+Hixby/23MSufHRbNkrO5KNT+0Kk1XWyNnXDx8na7c1GSwN2XFycBg0apOLi4oB1Bw4ckCSN\nGDEi5Pbp6en6+OOPVVpaqhtvvLHFus8++0yGYWjAgAHt7qex0VRjY+uHHzmpoaFR9fXu/KNKbx1D\nb9a5tS87kY328eL+Qs/h48W+vdizXdyWjZKz+ejUvhBpdZ2sTd3IqN0WywevT5gwQcePH9e2bdua\nl5mmqXXr1ikmJibgOoeXmjhxokzT1MqVK9XY+H9PyOHDh7Vnzx790z/9k3r37m21JQBwHNkIAIHI\nRgCRxr9o0aJFVjYYNmyYdu7cqQ0bNqiyslLHjh3Ts88+q3fffVePPfaYxowZI0kqLS3V3r17Jf3f\nYTzJycmqrq7Wli1b9Je//EV1dXX64x//qCeffFLR0dH69a9/rcTExHb3UlNTZ6X1sPH5DMXGRuvC\nhYuu+xSJ3jqG3qxza19N4uNjbL0/srFz3L6/BEPP4ePFvr3YcxM789FN2Sg5k49O7QuRVtfJ2tQN\nHydrtzcbLQ/YUVFRuvPOO1VeXq4dO3Zo9+7diouL09y5czVp0qTm2+Xn52vJkiXq3bu3Ro8e3bz8\nu9/9rgYOHKgPP/xQW7Zs0eHDh/Xd735Xv/rVr5SammqlFde+iHTzH1V66xh6s86tfTWxe8AmGzvH\n7ftLMPQcPl7s24s9N7EzH92UjRID9uVc18na1A0fLwzYhtnWNRRc7PTpSqdbCCoqyqfExHidO1ft\nuu8G0FvH0Jt1bu2rSVJST6db6DJuzcbWuH1/CYaew8eLfXux5ybko72c2hcira6TtakbPk7Wbm82\nuvcCYgAAAAAAeAgDNgAAAAAANmDABgAAAADABgzYAAAAAADYgAEbAAAAAAAbMGADAAAAAGADBmwA\nAAAAAGzAgA0AAAAAgA0YsAEAAAAAsAEDNgAAAAAANmDABgAAAADABgzYAAAAAADYgAEbAAAAAAAb\nMGADAAAAAGADBmwAAAAAAGzAgA0AAAAAgA0YsAEAAAAAsAEDNgAAAAAANmDABgAAAADABgzYAAAA\nAADYgAEbAAAAAAAbdGjALi8v1+LFizV27Filp6crOztbGzZs6FADy5Yt0+DBg/XOO+90aHsAcAuy\nEQACkY0AIkmU1Q1qa2s1c+ZMHTlyRFOmTFFqaqq2b9+uhQsX6syZM5o1a1a772vfvn1au3atDMOw\n2gYAuArZCACByEYAkcbygJ2Xl6dDhw5p2bJlysrKkiTl5OQoNzdXK1euVHZ2tvr169fm/VRWVmr+\n/Pnq1q2b6urqrHcOAC5CNgJAILIRQKSxfIh4YWGhkpKSmkOySW5ururq6rRly5Z23c8vfvELmaap\nyZMnW20BAFyHbASAQGQjgEhjacCuqqpSWVmZhg8fHrCuaVlRUVGb97Np0ybt2LFDS5cuVc+ePa20\nAACuQzYCQCCyEUAksjRgnzx5UqZpqn///gHrevToofj4eB09erTV+/j888/1n//5n5o+fbpuuukm\na90CgAuRjQAQiGwEEIksDdiVlZWSpPj4+KDrY2NjVVNTE3L7xsZGzZ07V1dddZUeeeQRK6UBwLXI\nRgAIRDYCiESWTnJmmmab6/1+f8j1zz//vEpKSvT6668rOjraSmkAcC2yEQACkY0AIpGlAbvpHcja\n2tqg62trazVw4MCg6z788EP95je/0cyZM9W3b1+dO3dOkprfuayurta5c+d05ZVXtvvyCz6fIZ/P\nfZdq8Pt9Lf51E3rrGHqzzq19dQWysfO8uL/Qc/h4sW8v9mw3t2Wj5Ew+OrUvRFpdJ2tTNzJqt5el\nATslJUWGYejEiRMB66qqqlRTUxP0ezaS9Pbbb6uhoUEvvPCCVq9e3WKdYRiaM2eODMPQm2++qauu\nuqpd/fTqFe/qayEmJMQ63UJI9NYx9GadW/uyE9loHy/uL/QcPl7s24s928Vt2Sg5m49O7QuRVtfJ\n2tSNjNptsTRgx8XFadCgQSouLg5Yd+DAAUnSiBEjgm77gx/8QCNHjgxYvmnTJm3evFlz587V9ddf\nrz59+rS7n7Nnq135KY3f71NCQqwqKmrV0NDodDst0FvH0Jt1bu2rSWJi8O8EdgTZ2Hlu31+Coefw\n8WLfXuy5iV356LZslJzJR6f2hUir62Rt6oaPk7Xbm42WBmxJmjBhgpYvX65t27Y1X9PQNE2tW7dO\nMTExAdc5bJKSkqKUlJSA5R988IEk6frrr9fNN99sqZfGRlONja1/v8dJDQ2Nqq935x9VeusYerPO\nrX3ZjWy0hxf3F3oOHy/27cWe7eSmbJSczUen9oVIq+tkbepGRu22WB6wp0+frs2bN2v+/PkqLi5W\namqqtm7dqvfee0/z5s1rfiextLRUpaWlSktLU1pamu2NA4CbkI0AEIhsBBBpLA/YMTExysvL0/Ll\ny7V582ZVV1crNTVVzzzzjO6+++7m2+3cuVOrVq3S7NmzCUoAlz2yEQACkY0AIo1htnUNBRc7fbrS\n6RaCioryKTExXufOVbvu0AV66xh6s86tfTVJSurpdAtdxq3Z2Bq37y/B0HP4eLFvL/bchHy0l1P7\nQqTVdbI2dcPHydrtzUb3nt8cAAAAAAAPYcAGAAAAAMAGDNgAAAAAANiAARsAAAAAABswYAMAAAAA\nYAMGbAAAAAAAbMCADQAAAACADRiwAQAAAACwAQM2AAAAAAA2iHK6AQAAcHmqq6tTScnBTt+P3+9T\nQkKsKipq1dDQ2Kn7Gjr0BkVHR3e6JwAAgmHABgAAXaKk5KAm5T2nqOS+TrciSao/fkqvTn1Y3/72\nSKdbAQBcphiwAQBAl4lK7qvobw5wug0AAMKC72ADAAAAAGADBmwAAAAAAGzAgA0AAAAAgA0YsAEA\nAAAAsAEDNgAAAAAANmDABgAAAADABgzYAAAAAADYgAEbAAAAAAAbMGADAAAAAGADBmwAAAAAAGwQ\n1ZGNysvLtWLFCr311ls6c+aMrr76ak2bNk0/+tGPLG176tQp9ezZU6NHj9bPfvYzDRo0qCPtwCXq\n6upUUnKww9v7/T4lJMSqoqJWDQ2NlrcfOvQGRUdHd7g+0FlkIwAERz4CiBSWB+za2lrNnDlTR44c\n0ZQpU5Samqrt27dr4cKFOnPmjGbNmhVy27q6Ok2dOlWffvqpJk6cqGHDhuno0aN66aWX9Pbbbys/\nP1/XXXddpx4QnFNSclCv7F2jq65J7vidfNGxzY6VHdePdZ++/e2RHa8NdALZCADBkY8AIonlATsv\nL0+HDh3SsmXLlJWVJUnKyclRbm6uVq5cqezsbPXr1y/otuvWrdORI0e0ZMkSTZw4sXl5ZmamcnJy\n9Mwzz2jNmjUdfChwg6uuSVbq0G863QYQdmQjAARHPgKIJJa/g11YWKikpKTmgGySm5ururo6bdmy\nJeS2f/nLXxQTE6Mf/vCHLZYPGTJE1157rf76179abQcAXIFsBIDgyEcAkcTSJ9hVVVUqKytTRkZG\nwLrhw4dLkoqKikJuv3z5cp05c0aGYQSsC7UcANyObASA4MhHAJHG0oB98uRJmaap/v37B6zr0aOH\n4uPjdfTo0ZDb9+nTR3369AlYvmnTJp0+fVq33367lXYAwBXIRgAIjnwEEGksDdiVlZWSpPj4+KDr\nY2NjVVNTY6mBw4cPa/HixYqKitJDDz1kaVsAcINIzcbOXjngUp29isCluKIA4B6Rmo8AIpelAds0\nzTbX+/3+dt/fwYMHdf/996umpka/+MUvNGTIECvtyOcz5PO579Agv9/X4l836crenH68fr9PUVFd\n00Ok/kw7w619dYVIzcaiohJNyntOUcl9u7xWe9UfP6U3ZjyiESO6/ooCXtzHw92zG5+brvxb8fU6\nl/4bqSI1Hy/l1L4QaXWdrE3dyKjdXpYG7KZ3H2tra4Our62t1cCBA9t1X7t379ajjz6qL7/8UgsX\nLtTkyZOttCJJ6tUr3tXfvUlIiHW6hZC6oreEhNgOX2bLrvqJicHfIbezhlt1RW91dXX68MMPbb/f\n9kpPT/fEJ5GRmo0JCbGKSu6r6G8O6PJaVoQjC75ez2vC1bMbnxv2j/CK1HwMxql9obN1w/FawO6/\n9159rqnrjdptsTRgp6SkyDAMnThxImBdVVWVampqgn7H5utefvllPf300/L7/Xr22Wf1/e9/30ob\nzc6erXbtJ9h2Hepot67sraIi+B/PcKmoqNW5c9Vdct+R+jPdv/8D/fbt1Z27tnkHHSs7rikVs7rs\nk0g7X2BHajY6/TsfSldmwaXcnAuhhLtnN+4j7B9tIx/t5dS+YFfd/fs/0P97cL4Ud4WN3V2i5rx2\nPb/Ulr/3Xn+uqevu2u3NRksDdlxcnAYNGqTi4uKAdQcOHJAkjRgxotX7ePHFF7V06VJdccUVWrVq\nlUaNGmWlhRYaG001NrZ+6JGTGhoaVV/vzj+qXdGb0y8gwvF8R+LP1Mlrm7v5+b5UpGaj07/zoYR7\nv/HKfnqpcPXsxn2krcdu17kFOK/AVyI1H4NxKis6W7ehofGr4bpn4Mnm7GL3c+PV55q63qjdFksD\ntiRNmDBBy5cv17Zt25qvZ2iaptatW6eYmJiAaxxe6s9//rN++ctfKjExUXl5ebr22ms73jkAgro8\nsAAAEkVJREFUuAjZCFweSkoOuurcAvXHT+nVqQ/r29/u+vMKdBXyEUAksTxgT58+XZs3b9b8+fNV\nXFys1NRUbd26Ve+9957mzZvXfCmF0tJSlZaWKi0tTWlpaTJNU08//bQk6fbbb9dHH32kjz76KOD+\nJ0yY0MmHBADhRzYClw83nlvAy8hHAJHE8oAdExOjvLw8LV++XJs3b1Z1dbVSU1P1zDPP6O67726+\n3c6dO7Vq1SrNnj1baWlpKisr09///ndJUkFBgQoKCoLe/1133SWfz71nhQOAYMhGAAiOfAQQSSwP\n2JKUmJiop556Sk899VTI28yZM0dz5sxp/v+gQYN06NChjpQDOq2z36nr7HfpvPz9ObQf2QgAwZGP\nACJFhwZswGtKSg7qlb1rOnc27A5eguxY2XH9WPd5+vtzAAAA6FpWPxDqyAdAfOjT9RiwETGcPBs2\nAPfgLNEAADcqKTmo8Q/9vEsvifb7FUv40KeLMWAHweHEAHD54izRAADX6uJLoqHrMWAHweHEAHB5\n4yzRAACgKzBgh8DhxAAAt3DjYe0SR1wBAPB1DNiAw/hKAoC2uO2wdolD2xG5OBEVLjfh2KelyNmv\nGbABh/GVBADtwWHtgDtwIipcbrp8n5Yiar9mwPYYPu28PPGVBAAAPIQTUeFywz5tGwZsj+HTTgAA\nAABwJwZsD+LTTgAAAABwHwZsAAAAAK7DCeXgRQzYAAAAgMtF4rDJCeXgRQzYAAAAgMtF7LDpwMm3\nIvHNDNiHARsAAADwAs70HBYR+2aGAy7HNzMYsAEAAADgUryZERaX45sZDNgAAAAAAGdcZm9m+Jxu\nAAAAAACAywEDNgAAAAAANmDABgAAAADABgzYAAAAAADYgAEbAAAAAAAbMGADAAAAAGCDDg3Y5eXl\nWrx4scaOHav09HRlZ2drw4YN7dq2sbFRL774orKyspSenq6xY8dq+fLl+vLLLzvSCgC4BtkIAMGR\njwAiheXrYNfW1mrmzJk6cuSIpkyZotTUVG3fvl0LFy7UmTNnNGvWrFa3X7RokV577TVlZmZq+vTp\nKikp0erVq/XRRx/phRde6PADAQAnkY0AEBz5CCCSWB6w8/LydOjQIS1btkxZWVmSpJycHOXm5mrl\nypXKzs5Wv379gm5bVFSk1157TZMmTdKTTz7ZvDw5OVm//vWvtWPHDmVmZnbwoQCAc8hGAAiOfAQQ\nSSwfIl5YWKikpKTmgGySm5ururo6bdmyJeS2GzdulGEYmjFjRovlM2bMUFRUlDZu3Gi1HQBwBbIR\nAIIjHwFEEksDdlVVlcrKyjR8+PCAdU3LioqKQm5fVFSknj17KjU1tcXy2NhYfetb39KHH35opR0A\ncAWyEQCCIx8BRBpLA/bJkydlmqb69+8fsK5Hjx6Kj4/X0aNHQ25/4sSJoNtKUr9+/VRRUaGqqior\nLQGA48hGAAiOfAQQaSwN2JWVlZKk+Pj4oOtjY2NVU1PT6vZxcXEht5W+OhEGAHgJ2QgAwZGPACKN\npZOcmabZ5nq/39+h7ZvWtbb91/l8hnw+o923by+/36djZcdtv9/2OFZ2XP4BPkVFBX/vg96Co7eO\n8XJvbhIp2fh1fr9P9cdPdXkdK+qPn5Lf3/p+47a+vdiz5M2+L9ee3exyzEe/3yfVnO/UfbSq5nzQ\nn3mk1XWyNnUvo9qt7F9dxdKA3fTuY6h3CmtrazVw4MBWt79w4ULIbaWvDhdqr969239bKzIyblVG\nxq1dct+dRW8dQ28d4+be3CRSsvHrMjJu1TkP7h9e7NuLPUve7NuLPbvZ5ZiPGRm3yizd2+n7oa57\na1M3Mmp3FUujfEpKigzD0IkTJwLWVVVVqaamJuT3ZJq2D7at9NV3dBITExUdHW2lJQBwHNkIAMGR\njwAijaUBOy4uToMGDVJxcXHAugMHDkiSRowYEXL79PR0nT9/Xp9//nmL5TU1NTpy5Eir2wKAW5GN\nABAc+Qgg0lg+GH3ChAk6fvy4tm3b1rzMNE2tW7dOMTExAdc4vNTdd98t0zS1du3aFsvXr1+vhoYG\n/fCHP7TaDgC4AtkIAMGRjwAiiX/RokWLrGwwbNgw7dy5Uxs2bFBlZaWOHTumZ599Vu+++64ee+wx\njRkzRpJUWlqqvXu/Op6+T58+kqTk5GR98cUX2rBhgz7++GNVVVXplVde0YsvvqixY8dqzpw59j46\nAAgTshEAgiMfAUQSywN2VFSU7rzzTpWXl2vHjh3avXu34uLiNHfuXE2aNKn5dvn5+VqyZIl69+6t\n0aNHNy8fO3asoqOj9ec//1lbt27V+fPnNXXqVC1cuNDSWSABwE3IRgAIjnwEEEkMs63rJwAAAAAA\ngDZ586KKAAAAAAC4DAM2AAAAAAA2YMAGAAAAAMAGDNgAAAAAANggyukGLkfjxo3T559/rgceeECP\nPPKIo70sWLBABQUFLZYZhqGePXtq0KBBysnJcfwakm+99ZYKCgpUXFys06dPKz4+XsOGDdOPf/xj\nZWRkhL2flStXauXKlS2W+Xw+de/eXQMGDNBtt92m3NxcXXnllWHvLVR/wUyfPl0LFiwIQ0f/p6Cg\noM2ahmHo/fffV48ePcLUFbzATbkZihfyNBS35Wxr3J7Bobg5m+GscOWb0xkV7pxxMiuc/H138rXW\n/v37tXHjRu3fv18nT55UY2OjkpOTNWbMGE2bNk3f+MY3bK23YsUKrVq1SkuXLtUPfvCDoLdpej7m\nzJnjmsv2MWDbbN++ffr8888VHx+vDRs26KGHHlJUlLNPs2EY+td//Vddc801kqT6+nqVl5dr9+7d\nWrBggY4dO6bZs2eHva/q6motWLBAf/jDHzRkyBDdc8896tu3r06cOKHCwkLNnj3bsRcihmEoJydH\no0aNkiQ1NDSosrJSBw4c0Nq1a1VQUKCXX37Z9iDpaH/BDBo0KIwdtXTHHXdo3LhxIdfHxsaGsRu4\nnRtzMxS35mkobs7Z1rg9g0NxezYj/MKdb05klJM542RWOP37Hs7XWhcvXtTSpUv10ksv6aqrrlJm\nZqauvvpqmaapkpISbdy4Ufn5+frVr36lzMxM2+oahiHDMNp1O1cxYavHH3/cHDp0qLlixQozLS3N\n3Lp1q6P9zJ8/3xw8eLC5b9++gHUNDQ1mdna2OXz4cLOioiLsvT388MPm4MGDzRdeeCFgXV1dnTlj\nxgwzLS3NfOmll8La14oVK8zBgwebBQUFQdfv2bPHHDJkiJmZmWk2NDSEtTfTbLs/J23cuNFMS0sz\nV6xY4XQr8BC35WYobs7TUNyas61xewaH4uZshnPCmW9OZZRTOeNkVjj5++7Ea62lS5eaaWlp5hNP\nPGHW1dUFrD927JiZkZFh3njjjeaxY8dsq9ue59mNrz35DraNqqurtXPnTt1www3Nh+Dk5+c73FVo\nPp9PN998s+rq6vTZZ5+FtfaePXu0Y8cO3XHHHbrvvvsC1nfr1k1LlixRVFSUXnrppbD21pZbbrlF\nM2bM0GeffabNmzc73Q7gaV7LzVCczNNQvJyzrSGD4RVuyreuyig35wxZYY/Dhw/rxRdf1JAhQ/Tk\nk0+qW7duAbdJTk7WE088oQsXLui1115zoEt3YcC20e9+9zvV1tbqlltu0YABAzR8+HC9//77Kisr\nc7q1kI4ePSq/36+UlJSw1t20aZMMw9DUqVND3iY5OVmbN292ZSjec889Mk1Tb775ptOtAJ7mxdwM\nxak8DcXrOdsaMhhe4LZ864qMcnvOkBWdt3HjRknSQw89JJ8v9Oj4ve99T2vWrNFPf/rTcLXmWu78\nkptHbdiwQYZh6M4775QkZWVlqaioSPn5+fr5z3/uaG+VlZU6d+6cJMk0TZWXl2v79u3atWuXZs2a\npcTExLD2c/DgQfn9fqWnp7d6u6bvELlNamqqunfvrpKSEsd6qK6ubv6ZBhPun+mlLly4ELI3J/uC\n+7g5N0NxW56G4vWcbY0bMjgUN2czwsupfAtnRrk9Z7o6K5z8fQ/Xa6133nlHhmHo5ptvbvV2hmHo\nlltusa3upVp7nqurq7ukZmcwYNvkk08+UVFRkQYPHtx8QoOsrCw988wzKiws1GOPPabo6GhHejNN\nUw8++GDQdaNGjdIDDzwQ5o6kU6dO6corrwx6mIlXXHHFFTp79qwjtU3T1OLFi7V48eKg650+U/fa\ntWu1Zs2agOWGYejQoUMOdAQ3cnNuhuLGPA3lcsjZ1jiZwaG4PZsRPk7lW7gzygs501VZ4fTve7he\nax0/flyJiYnq3r17wLpgQ6/f71dCQoJt9dt6niX3neSMAdsmb7zxhgzD0Pe///3mZX379tWoUaP0\n/vvva+vWrY5dvsUwDM2bN09paWmSvtpRKyoq9Ne//lX5+fmaOHGiXn75ZfXq1StsPfn9fjU2Noat\nXle4ePGiY7/QhmEoNze31XcK4+LiwthRS9nZ2crOznasPrzBzbkZihvzNJTLIWdb42QGh+L2bEb4\nOJVv4c4oL+RMV2WF07/v4Xqt1djYGPJnHOxT7f79++uPf/yjbfXbep737NmjtWvX2lbPDgzYNmho\naNCWLVskSenp6friiy+a1910003at2+fXnnlFUdfKA4dOlTf+c53WizLzMxUamqqFi9erOeff15P\nPPFE2Prp16+fPvvsM128eNHV73qG0tDQoIqKCvXr18+xHq699to2D9dxSkpKimt7gzt4ITdDcVue\nhuL1nG2NGzI4FDdnM8LD6XwLZ0a5PWe6Oiuc/H0P12ut5ORkffrpp0F/xuvXr2/x/8cff7xLemjt\neT5x4kSX1OwMBmwbvPXWW/rHP/4hwzA0bdq0Fuua3jE7ePCgDh06pOuvv96JFkPKzs7W4sWL9cEH\nH4S17ne+8x2VlZXpf/7nfzR69OiQt/uP//gPVVdX6/HHH1f//v3D2GHrDh06pPr6eg0bNszpVgBP\n8nJuhuJUnobi9ZxtDRkMN3NrvnVFRrk9Z8iKzmv6Ge/du1ff+973Wqz7+tAbHR3t+iMawoEB2wZN\nhwHdf//9QU/yUFBQoDfffFOvvPKKnnrqKQc6DK3plyDch9ndddddys/P129/+9uQgXzq1CkVFBQo\nLi5O//Vf/xXW/tpSWFgowzCUmZnpdCuAJ3k5N0NxKk9D8XrOtoYMhpu5Nd+6IqPcnjNkRef9y7/8\ni1599VW98MILuvXWW13zN87NGLA76cyZM9qzZ48SEhI0e/ZsxcTEBNxm4MCB2rVrl373u99p3rx5\nio+Pd6DT4JpOvf/P//zPYa07atQojRs3Tjt37tSaNWsCrp1YVVWln/3sZ6qvr9fs2bNddaKjpkO7\nrr32Wo0fP97pdgDP8XpuhuJUnobi5ZxtDRkMN3NzvnVFRrk5Z8gKewwdOlS5ublau3at5s2bpyef\nfFKxsbEtblNXV6f169fr5MmT6tu3r0OdugcDdidt3LhR9fX1mjhxYtAQlaTrrrtOY8aM0TvvvKPC\nwkL95Cc/CWuPpmlqz549On78ePOyL7/8Uu+++6527NihAQMGaObMmWHtSZKWLFmi8+fPa9myZdq2\nbZvGjx+vXr166dNPP1VhYaHOnj2ryZMnBxxeFQ6maWr//v3N1/trbGxURUWFDhw4oD/84Q/q06eP\nVq5c2er1AMPZXzDdunVrvjQI4CZeyM1Q3Jqnobg5Z1vj9gwOhWyG0/nmREY5mTNOZkUk/b4/+uij\n8vv9WrNmjfbs2aPx48frW9/6lnw+n44cOaLf//73OnPmjAYMGKCFCxfaWts0TVvvLxwYsDtp06ZN\n8vv9mjx5cqu3mzFjht555x29+uqrYX+haBiGVq9e3WJZ9+7dNWDAAE2bNk333XefrrjiirD2JEk9\ne/bUunXrtHXrVm3atEn5+fn6xz/+oR49eig9PV333nuvY58EGYah119/Xa+//nrz/+Pi4vTNb35T\nDzzwgKZNm+bIcxaqv2B69uzpSKgbhsHhQ2iVF3IzFLfmaShuztnWuD2DQ3FzNiM8nM43JzLKyZxx\nMiuc/H0P92stwzD0yCOP6K677tLGjRu1d+9ebdu2TV9++aV69+6t0aNHa/z48Ro3bpztb2a053G6\n7bWnYXrxbQEAAAAAAFzGXcdWAQAAAADgUQzYAAAAAADYgAEbAAAAAAAbMGADAAAAAGADBmwAAAAA\nAGzAgA0AAAAAgA0YsAEAAAAAsAEDNgAAAAAANmDABgAAAADABgzYAAAAAADYgAEbAAAAAAAbMGAD\nAAAAAGCD/w8o/bHoeNbVdwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ed63358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def show_soft():\n",
    "    colors_list = ['#9BCC93', '#1A9481', '#003D5C']\n",
    "    categories_list = ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H']\n",
    "    vals_list = [[.3, .1, .8, .4, .2, .6], [.5, .2, .1, .9, .4], [.5, .2, .9, .3, .15, .7, .5, .1]]\n",
    "    plt.figure(figsize=(10,5))\n",
    "    for i in range(len(vals_list)):\n",
    "        vals = vals_list[i]\n",
    "        soft_vals = softmax(vals)\n",
    "        plt.subplot(2, len(vals_list), 1+i)\n",
    "        plt.bar(range(len(vals)), vals, align='center', color=colors_list[i])\n",
    "        plt.xticks(range(len(vals)), categories_list)\n",
    "        plt.subplot(2, len(vals_list), 1+i+len(vals_list))\n",
    "        plt.bar(range(len(vals)), soft_vals, align='center', color=colors_list[i])\n",
    "        plt.xticks(range(len(vals)), categories_list)\n",
    "        plt.ylim(0, 1)\n",
    "    plt.tight_layout()\n",
    "    file_helper.save_figure('softplus-plots')\n",
    "    plt.show()\n",
    "\n",
    "show_soft()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
